IM 8.7.2 Lesson: Multiplying Powers of Ten

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0+ZMsWdX+zcuTPKBIH7Ly4udivcRYsWRZkgEJMAs6qcP/ohwFQTAowrMK0GQ4sAMxTTc0WAqSAEGAGm1WBoEWCGYnquCDAVhAAjwLQaDC0CzFBMzxUBpoIQYASYVoOhRYAZium5IsBUEAKMANNqMLQIMEMxPVcEmApCgBFgWg2GFgFmKKbnigBTQQgwAkyrwdAiwAzF9FwRYCoIAUaAaTUYWgSYoZieKwJMBSHACDCtBkOLADMU03NFgKkgBBgBptVgaBFghmJ6rggwFYQAI8C0GgwtAsxQTM8VAaaCEGAEmFaDoUWAGYrpuSLAVBACjADTajC0CDBDMT1XBJgKQoARYFoNhhYBZiim54oAU0EIMAJMq8HQIsAMxfRcEWAqCAFGgGk1GFoEmKGYnisCTAUhwAgwrQZDiwAzFNNzRYCpIAQYAabVYGgRYIZieq4IMBWEACPAtBoMLQLMUEzPFQGmghBgBJhWg6FFgBmK6bkiwFQQAowA02owtAgwQzE9VwSYCvJvAYb2Y6Ff6PuWaKs2duzYKF1zkNehQ4dcWzX0hUTfQnQNCvnyuxIh5xj6Iqf/RFciNAsuLCyUAQMGyIEDB0JK+5tvNEMdPXr0b303f/tDQOP48eMyf/581xdy+fLlUZ4pWhGuXLlSmjRpIugLid6UoV9osYhxgm7cQ4cO/a2Xasi4GDPIFTXUvXv3v9bYFg8FpMcgC3mhALZu3eoarz755JPuYYSMB98QZf/+/XLbbbdJjx49XENUNCQNGRf+AetJkyZJixYtXM64j5AxE76XLl0qrVu3ds2KUeyJ34d8X79+veumjN6baIgaMlbCNzqfjxw50um7ZcuWKDGPHDkir7/+umRnZ7uJIsYzRfPnkpIS19h2/PjxrsdpQoNQ72ABOtp36dJFHnzwQWejQXSoePCLMfPTTz+5hQYmw82bN/+Bl6WuwC666CLXoh0dhxcsWBD0mjt3rutWXadOHenZs6e89tprQeMhn3nz5skrr7zieiViFps5c6abRUPmigkBcQcPHizVqlVzOcfQFzmhYXCNGjVk+PDhUfRFTAysRo0auYkJ+obUNuF7xowZbtWHXNEBPfH7kO9z5syR++67TypUqCDYQcR4pgDmE088IZUqVZKBAwfK7Nmzg+eKvKZOnSr16tVzqzBojZoOqS38gw/otN65c+eyA6xcuXJSq1YtycvLkyuuuCLo1bRpU6lbt64kJydLZmam4OfQMZEXBldKSoqkp6dLw4YNpVmzZkHjwj/iIl5qaqrk5ORE0RdaQlcMsKysrCj6IuZll13m8kSu0Df0M4X/Bg0aSNWqVV0toaZixMzNzZXatWsLJn2AM8aYufzyy139JCUlSeXKld1WMnSuqF9M9mlpaa6GoXWsMVOxYkXJz88vO8BQdOPGjZOvv/7a/Scs3UJdGzZsEGxx8FDuv/9+wdYjVKyEX+T1+eefu311+/bt5dNPP5VNmzYFjQv/ONjGNhkPf9myZVH0Rc5Y+aH4JkyYEEVfxFy8eLFb4WKLjvOahPYh31esWCGDBg1ykxNqKmSshO9169bJCy+84FbV0DnGmPnyyy/dMwU4H330UVm7dm3wXDdu3Oi2rVdddZXb0kHrGGMGfCgoKHCrPmjuv0rdQmJpiiUjzmywzw154UwGN9amTRu3LD569GjQeMjlxIkT7hCyT58+DmI4O8EeP2Se8I/9/MSJE387o8F9hIyZ8P3RRx9Jq1at3JI/hr6I+8UXX0i3bt2kb9++7owxcS8h33ft2iWPPPKING/e3NVUyFgJ34cPH3bbHJyBYVKK8UxxbvzJJ584UL/00kty8ODB4HUEFkDfa665xh0vwY4xZpAraugvnYFVqVJFFi5cKPjkIfQLh56JTyFxVoMCCP3CASEKDwfMN/BrFEHk5tcogsjqnAIciU8hMSH+Jz6FjPXJPXL9y59CEmD2xed/jWLnzp1RJghk8p/4GgUBZl9DCY8EWEIJkVK3kASYCmRlEWBWSv65n//k98DwoQG+BxZj10KAaQ0QYNxCajUYWlyBGYrpuSLAVBACjADTajC0CDBDMT1XBJgKQoARYFoNhhYBZiim54oAU0EIMAJMq8HQIsAMxfRcEWAqCAFGgGk1GFoEmKGYnisCTAUhwAgwrQZDiwAzFNNzRYCpIAQYAabVYGgRYIZieq4IMBWEACPAtBoMLQLMUEzPFQGmghBgBJhWg6FFgBmK6bkiwFQQAowA02owtAgwQzE9VwSYCkKAEWBaDYYWAWYopueKAFNBCDACTKvB0CLADMX0XBFgKggBRoBpNRhaBJihmJ4rAkwFIcAIMK0GQ4sAMxTTc0WAqSAEGAGm1WBoEWCGYnquCDAVhAAjwLQaDC0CzFBMzxUBpoIQYASYVoOhRYAZium5IsBUEAKMANNqMLQIMEMxPVcEmApCgBFgWg2GFgFmKKbnigBTQQgwAkyrwdAiwAzF9FwRYCoIAUaAaTUYWgSYoZieKwJMBSHACDCtBkOLADMU03NFgKkgpQIsJSVFnnnmGVm9erVrW47W5aEuNOhEG/rGjRu7tvCffvppsFiJHFatWuV6JaJzNFqlow194m8h3xF3zJgxgi7OyDmGvsjn1Vdflfr168vzzz8vMfRFzLfeektatmzpunOjY3VIXRO+lyxZIv3795d69erJe++9FyVmSUmJjB07VtDNHjrHeKafffaZzJo1S7KysuThhx8W3ENCg1DvyOuDDz6QK664Qm699VaB1mvWrAkeF3xAN/AuXbq4buuKrn9ZpQKsXLlygj53aEffunXroBeKPDc3Vy655BKpUaOGtGjRImg85ANo4UGkpqZKRkaGNGvWLHhMxIWe1apVc3GRcwx9ERfArFChgnuPoS9iNmzYUNLS0iQ9PT2avnl5eZKZmSnJycnSpEmTKM+0efPmbqxcdNFFkpOTE+WZYsxgwk9KSpLq1asL7gGah7xQq1deeaV7ppUrVxZoHTJewjfGKuLl5+eXHWAogLvuukumTp0q06dPD3pNmjRJioqK3OAqLCwUtEoPHXPKlCny4osvOlgCJFiZhI45bdo0QdzevXtLzZo1Xc4x9EVew4YNk9q1a8vgwYOj6IuYjz32mBtkKMAXXnghuL6I+dxzz0nXrl3dRIhVUehnCv8TJkyQO+64w4F6xIgR0cbMQw89JFWrVpVevXrJ+PHjg+eKWsU4adCggXTq1MnZqOnQGk+ePNmt5LEK27x5s78AK70zd8WKFd1y+PDhw3L06NGg1759+2TDhg1uVTRq1ChBd+XQMQ8dOiQ7d+6UW265xRX81q1bg8dETgcPHpRx48a5FQlyxn2EzhX+sV3FLD1nzpwo+iImtjkoOmw3tm/fHiXPLVu2yPDhw52+69evjxJzz549MnPmTKlVq5a8//77UZ7p/v375cMPP3THAoD27t27g+cKFkDfjh07yj333OPsI0eOBI+LXDFOCwoKyg6wKlWqyMKFC6O0ST958qTs2LFD2rVr51YlJ06c+ANlrX9x+vRpwQPp16+f3MBDfGt5nT8e4geR1TnlIb5qW+oZGAGmAllZZ8+elVOnTrltJLZVWAGeOXPGyv2/9VNcXCxt27aVRYsWSYwJAjdDgP3bR/J/+iMBpvIRYFyBaTUYWgSYoZieKwJMBSHACDCtBkOLADMU03NFgKkgBBgBptVgaBFghmJ6rggwFYQAI8C0GgwtAsxQTM8VAaaCEGAEmFaDoUWAGYrpuSLAVBACjADTajC0CDBDMT1XBJgKQoARYFoNhhYBZiim54oAU0EIMAJMq8HQIsAMxfRcEWAqCAFGgGk1GFoEmKGYnisCTAUhwAgwrQZDiwAzFNNzRYCpIAQYAabVYGgRYIZieq4IMBWEACPAtBoMLQLMUEzPFQGmghBgBJhWg6FFgBmK6bkiwFQQAowA02owtAgwQzE9VwSYCkKAEWBaDYYWAWYopueKAFNBCDACTKvB0CLADMX0XBFgKggBRoBpNRhaBJihmJ4rAkwFIcAIMK0GQ4sAMxTTc0WAqSAEGAGm1WBoEWCGYnquCDAVhAAjwLQaDC0CzFBMzxUBpoIQYASYVoOhRYAZium5IsBUEAKMANNqMLQIMEMxPVcEmApCgBFgWg2GFgFmKKbnigBTQUoFWFpammtBj47K6F8Y8tq0aZOUlJS4bspDhw6VjRs3Bo2HXLZt2ybo3Iymtvn5+bJmzZrgMREXHcCffvppadSokaxYscLdR0htE77RpLhp06auJ2UMfRF3yZIl0r59e6fxunXroui7evVqufvuu6Vx48auphL5h3wHqMePHy+ZmZmu7yZqK2Q8+N68ebOLlZ2dLU888YR89dVXwWOCBatWrZLWrVvL7bff7sYMGlLHyLVHjx7SrVu3snfmPv/886Vly5Zy8803S69evYJePXv2lGuvvVbS09PdwMbPoWPedNNN0r17d6levbq70LY8dEz4R9wmTZq4XJFzDH0Rt02bNpKRkSFoqBtDX8Ts3LmzoEFyVlaWFBYWRtEXz7FBgwaSmprqairGM8UkiLGSlJTkusvHeKY33nijdOrUScqXLy+5ubly/fXXB9cXeWHM4JnWqVNHYo0Z5FqzZk3p2LEjAZYoaAIs7KREgIXVlwDjFpJbyMBHA9xChjt64Rby/wMwLBNxbnLmzBn9l4GskydPCvbS7dq1k6KiIjlx4kSgSOr29OnTcvjwYenXr587o9m/f7/+MZB19uxZOXXqlDuHwlYOZwcx9EU6xcXF0rZtW3duEkNfxOQhfqBCEhEe4qu2pR7iE2AqkJVFgFkp+ed+9u7dK6NHj3ZnUjh0jvE6fvy4zJ8/X+rWrSvLly+PMikRYPpkCTB+jUKrwdDiCsxQTM8VAaaCEGAEmFaDoUWAGYrpuSLAVBACjADTajC0CDBDMT1XBJgKQoARYFoNhhYBZiim54oAU0EIMAJMq8HQIsAMxfRcEWAqCAFGgGk1GFoEmKGYnisCTAUhwAgwrQZDiwAzFNNzRYCpIAQYAabVYGgRYIZieq4IMBWEACPAtBoMLQLMUEzPFQGmghBgBJhWg6FFgBmK6bkiwFQQAowA02owtAgwQzE9VwSYCkKAEWBaDYYWAWYopueKAFNBCDACTKvB0CLADMX0XBFgKggBRoBpNRhaBJihmJ4rAkwFIcAIMK0GQ4sAMxTTc0WAqSAEGAGm1WBoEWCGYnquCDAVhAAjwLQaDC0CzFBMzxUBpoIQYASYVoOhRYAZium5IsBUEAKMANNqMLQIMEMxPVcEmApCgBFgWg2GFgFmKKbnigBTQQgwAkyrwdAiwAzF9FwRYCoIAUaAaTUYWgSYoZieKwJMBSHACDCtBkOLADMU03NFgKkgpQKsYsWK8uqrr7rmr0ePHpWQ1759+2TDhg2CZq+jRo0S9PYLGQ++Dx065BrL3nLLLdK1a1fZunVr8JiIe/DgQRk3bpw0a9bM5Yz7CJ0r/C9evFiaN28uc+bMiaIvYn722WdyzTXXyK233iro0Rgjzy1btsjw4cOdvuvXr48Sc8+ePTJz5kypVauWvP/++662QueKRswffvih1K9fX5577jnZvXt38FzRCBr6duzYUe655x5nHzlyJHhc5IpxWlBQIOhI7r9KBVhycrLcddddMnXqVJk+fXrQa9KkSa4jd3Z2thQWFsrEiRODxkM+U6ZMkRdffFFatGghubm58vzzzwePOW3aNBe3d+/eUrNmTZdzDH2R77Bhw6R27doyePDgKPoi5mOPPSaNGzd2E9MLL7wQXF/ExGDGhFSjRg0ZO3ZslJgTJkyQO+64Q9LT02XEiBHRxsxDDz0kVatWlV69esn48eOD54paxThp0KCBdOrUydmoaege8po8ebJrVIzJsMwAK1eunOs03KpVK2ndunXQq2XLlg4il1xyiSs8QCV0TKz2rrjiCklNTZWMjAw3Y4eOCf/Qs1q1ai4uwBlDX8TF5FChQgX3HkNfxGzYsKGkpaW5gY0VZwx985slqOIAABZgSURBVPLyJDMzUzABN2nSJEpMrGzRlfuiiy6SnJycKM8UYwaTQ1JSklSvXt2trkPri1q98sor3TOtXLmyQOvQMeEfYxXx8vPzyw6wlJQUeeaZZ2T16tWydu3aoNfKlSvdFgcPZNCgQfLpp58GjYd8Vq1aJcXFxdKtWzcn0NKlS4PHTMQdM2aMAwm2dTH0RVwcB2C7gRk0hr6I+dZbb7mZExovW7Ysir5LliyR/v37S7169eS9996LErOkpMSt9ipVquR0jvFMsT2fNWuWZGVlycMPPyy4B2ge8kJeH3zwgZv4cSwArdesWRM0JvIBH7D66tKlS9kBVqVKFVm4cKGcOXPG33Ka/3zy5EnZsWOHtGvXzm2rTpw4YR7Dd3j69Gl3vtevXz+5gYf4vjwmP/MQ30TGUp3wEF9lKfUMjABTgayss2fPyqlTp9w5GJbFO3fujDJB4P6x2mzbtq0sWrRIYkwQiEmAWVXOH/0QYKoJAcYVmFaDoUWAGYrpuSLAVBACjADTajC0CDBDMT1XBJgKQoARYFoNhhYBZiim54oAU0EIMAJMq8HQIsAMxfRcEWAqCAFGgGk1GFoEmKGYnisCTAUhwAgwrQZDiwAzFNNzRYCpIAQYAabVYGgRYIZieq4IMBWEACPAtBoMLQLMUEzPFQGmghBgBJhWg6FFgBmK6bkiwFQQAowA02owtAgwQzE9VwSYCkKAEWBaDYYWAWYopueKAFNBCDACTKvB0CLADMX0XBFgKggBRoBpNRhaBJihmJ4rAkwFIcAIMK0GQ4sAMxTTc0WAqSAEGAGm1WBoEWCGYnquCDAVhAAjwLQaDC0CzFBMzxUBpoIQYASYVoOhRYAZium5IsBUEAKMANNqMLQIMEMxPVcEmApCgBFgWg2GFgFmKKbnigBTQQgwAkyrwdAiwAzF9FwRYCoIAUaAaTUYWgSYoZieKwJMBSHACDCtBkOLADMU03NFgKkgBBgBptVgaBFghmJ6rggwFaRUgKHL8BtvvCE///yz/PLLL0GvY8eOuY67bdq0kSeeeEKOHj0aNB7yQW/EvXv3Sp8+faR79+6ye/duQVGEzBX+f/rpJ5k4caK0aNFCtmzZ4u4jZMyE748++si1vJ8/f34UfRH3iy++cJ3P+/btK999911QbRN57tq1Sx555BFp3ry5q6nE70O+Hz58WObOneu6raMDOWorZDz4Pn78uHzyySfSqFEjeemll+TgwYPBY4IF0Bddsh944AFnxxgzyBU1VFhYWPbO3KmpqTJu3Dj5+uuv3X/avHlzsPcNGzbI0qVL5fLLL5f7779f1q9fHyxWIg/k9fnnnzt4tW/fXj799FPZtGlT0Ljwj1XJk08+KQ0aNBAUewx9kfO8efOkSZMmMmHChCj6IubixYtdM90ePXq49vAJ7UO+r1ixQgYNGuQGNmoqZKyE73Xr1skLL7wg1apVczrHeKZffvmli1W7dm159NFHZe3atcFz3bhxo5SUlAiaMqOjPbSOMWbAh4KCAunatavLUdde/7JKXYGVK1dOatWqJXl5eXLFFVcEvZo2bSp169aV5ORkyczMFPwcOibywuyVkpIi6enp0rBhQ2nWrFnQuPCPuIiHCSInJyeKvtASulaoUEGysrKi6IuYl112mcsTuULf0M8U/jExVK1a1dUSaipGzNzcXAFILrroIqlRo0aUZ4rJHvWTlJQklStXdpNT6FxRv5gE09LSXA1D61hjpmLFipKfn192gOFhYJmIbeSCBQuCXlh+T548WerUqSM9e/aU1157LWg85IMVySuvvOJWCHgoM2fOFGyvQuYK/4g7ePBgN1sj5xj6IqeioiI3uIYPHx5FX8QcP368myRwNAB9Q2qb8D1jxgy31QBIoG/i9yHf58yZI/fdd5+bIMaOHRvlmb7++uvuuAVHPQMHDpTZs2cHzxW1OnXqVKlXr55bDUHrGGMGfGjZsqV07ty57AAD1XFz2OOePn066IU97tatWwWFju0VzsRCxzx58qTs379fbrvtNsEWB2c0p06dChoX/nGOMGnSJHcGhpxxH6FzhX9sp1q3bi1vvvlmFH0RE0cB1113ndtufP/991HyxFnmyJEjfztjjKHtkSNHBEDJzs6W4uLiKM/0xx9/dNu5xo0bu4kC53ChcwUL9uzZI126dJEHH3zQ2TiPCxkXYwbnxtiy/qUzsCpVqsjChQvdzfl7TuufMah37Ngh7dq1E8xgOAQN/YLohw4dcsJcf/31sm/fPjl79mzQsPCPBzJlyhR3joCccR8xXhhYbdu2lUWLFkXRFzl99dVXrugGDBggBw4ciJGm+2Bm9OjRbsbevn17lJiYgDHZYwexfPnyKM8UE9/KlSvdlu7ll192k1LoZM+cOePGCc6ihg4d6rT+9ddfg4bFmEGuqCF82IZzR/9V6hlYAmC46dAv3GACYNjqxAIYZi2Q/QZ+jSLII+bXKILI6pxiNZQAGD7Vxq4l9MsHWKxJH7kSYN7TxcqHAPNEMf6RADMW9HfuCDAVgyswrsC0GgwtAsxQTM8VAaaCEGAEmFaDoUWAGYrpuSLAVBACjADTajC0CDBDMT1XBJgKQoARYFoNhhYBZiim54oAU0EIMAJMq8HQIsAMxfRcEWAqCAFGgGk1GFoEmKGYnisCTAUhwAgwrQZDiwAzFNNzRYCpIAQYAabVYGgRYIZieq4IMBWEACPAtBoMLQLMUEzPFQGmghBgBJhWg6FFgBmK6bkiwFQQAowA02owtAgwQzE9VwSYCkKAEWBaDYYWAWYopueKAFNBCDACTKvB0CLADMX0XBFgKggBRoBpNRhaBJihmJ4rAkwFIcAIMK0GQ4sAMxTTc0WAqSAEGAGm1WBoEWCGYnquCDAVhAAjwLQaDC0CzFBMzxUBpoIQYASYVoOhRYAZium5IsBUEAKMANNqMLQIMEMxPVcEmApCgBFgWg2GFgFmKKbnigBTQQgwAkyrwdAiwAzF9FwRYCpIqQBDY1s0QUUfQ/R+C3mhjdq2bdtc38KnnnpK0LQzZDz4RkPOgwcPSt++fQV9Iffu3Rs8JtpSofDQMRqdhtG3MIa+yHfZsmWucTB6fcbQFzG//PJLKSgokP79+7t+gqGfKfyjQfGoUaOcvqipGDHR0gxdq9EX8pNPPonyTNFLdcWKFYLGtugL+cMPPwTPFZ280KD42muvlSFDhjgbNR1aY+SKGvpLfSHT09Nl2rRprvsuBnfI65tvvpFVq1ZJ8+bNZcSIEbJz586g8ZALOgxv3LhRbrrpJrn66qtdE9aQOSZ8o3P0c889J7m5ubJ69eoo+iL222+/Lc2aNZOZM2dG0RcxMZg7deokN998s2A1ltAg5Dug+cADD0jTpk1dTYWMlfANUGJSysrKknfeeSfKM/3222/l3Xfflbp168rTTz/tOtsn7ifUOyaHDRs2uAbUgwYNchMUgBYqXsIvcr3xxhtdl/cyN7a94IIL5PLLLxd04e3WrVvQ65prrnFt79PS0iQnJ0fwc+iYmEXy8/OlUqVKUq1aNenQoUPwmMgJcdGCPiMjw+WMn0PnCv8AJmLiHcCOEbNFixaCBskx9W3fvr1bCaWmpjp9Y+TZuXNnB8zk5GQ3ScR4phgjV111lZQvX95BDPcQOlewABMSdmc1atQQaB2DD9ATk0PHjh3L3pn7vPPOE4gyePBgufvuu4Ned955p/Tu3VsqVqzoCgA/h4551113uW6/gEn16tXdEjV0TPhH3LZt28qll14qffr0cT/HiFtYWChYVQNeMfRFTr169ZLMzEwHbGwBYuSJTutYfUFf1FSMmHfccYcbXElJSW6bE2PMYAXUo0cPSUlJkVatWsnAgQOD54q8oG/VqlWlUaNGzo6VK8bpXwIYZutXXnlFDhw44DpYo4t1qAvL0C+++MKdW4wcOdKdY4SKlfCLvHAGhUEGwm/ZsiVYfomYeN+/f7+8+OKLkpeXJ+vXr4+iL+K+9957bos+e/bsKPoi5sqVKx0wb7nlFrfF+b0OoexNmzbJ0KFDnb6oqVBxfu93165dMmPGDKlZs6YsXrw4yjPF9ur999+XevXqybPPPivYZv3+nkLYODOGvti5YGLAdu7QoUPB4yJXjFOcp5Z5C4ll4oIFC9xhNw7qQl4//fSTK3CsTHCIf/z48aDxEofpgBgO8TGTAaIhc4RvHIKePHlSJk2a9NshMw71Q8eF/6VLl7pDfHwwE0NfxMR5SeIQH0UYI0+cbeIQH9vXrVu3Rol59OhRmTdvntu6fvzxx+6DmtC54oOvkpISd4g/YcIEOXLkSPBc8cEXzsG6dOniDvFho6ZD5gr/yPUvH+Lj7AKfWOHmQr8wqHfs2OEOB4uKitwNh44JYTBLYUl8A79GEURufo0iiKzOKb9GodqW+jUKAkwFsrLOnj3rPmKfMmWKO4DFp60xJgjcf3FxsTt7W7RoUZQJAjEJMKvK+aMfAkw1IcC4AtNqMLQIMEMxPVcEmApCgBFgWg2GFgFmKKbnigBTQQgwAkyrwdAiwAzF9FwRYCoIAUaAaTUYWgSYoZieKwJMBSHACDCtBkOLADMU03NFgKkgBBgBptVgaBFghmJ6rggwFYQAI8C0GgwtAsxQTM8VAaaCEGAEmFaDoUWAGYrpuSLAVBACjADTajC0CDBDMT1XBJgKQoARYFoNhhYBZiim54oAU0EIMAJMq8HQIsAMxfRcEWAqCAFGgGk1GFoEmKGYnisCTAUhwAgwrQZDiwAzFNNzRYCpIAQYAabVYGgRYIZieq4IMBWEACPAtBoMLQLMUEzPFQGmghBgBJhWg6FFgBmK6bkiwFQQAowA02owtAgwQzE9VwSYCkKAEWBaDYYWAWYopueKAFNBCDACTKvB0CLADMX0XBFgKggBRoBpNRhaBJihmJ4rAkwFIcAIMK0GQ4sAMxTTc0WAqSAEGAGm1WBoEWCGYnquCDAVpFSAVapUSebOneuaoKKxZMgL/Rm//vprad26tTz22GOu22/IePB97NgxQRNUtJ9H89VvvvlG0GA3ZFz4/+GHHwSNSK+88krZuHFjFH2R0wcffOBauaEBK7oph8wz4XvNmjXStWtXue2221zn6MTvQ76jv+iIESOcvqipkLESvtFtHR3PL7vsMvnoo4+iPFM0sl22bJk0bNjQdXrft29f8FzREBmtADt37iz33Xefs2OMGeTap08fKSwsLHtn7qSkJOnZs6c8+uijDioAS6hr5MiRcs8990hWVpZrW/7II48Ei5XIYfTo0TJ8+HBp1KiR1K9f37WjT/wt1PuYMWMEca+++mqX67333htFX+Rz6623So0aNdwzjaEvYt55552Sk5MjTZo0kWHDhgV/pog5ZMgQ14G8WrVqrqZCPcvf+33ooYdcc+RLL73UwTrWmLn99tsFCw3UE+7h9/cUwkZeeI516tSR5s2bO61R0yFiJXzCPzqtN23a1OW5efNmXXr9r1XqCuzcc891dO/QoYODSn5+frD3du3auRkzJSVFatWq5Tp0h4wH38gLK7709HTJyMhwq5PQMeG/ffv2bqYuX768K4IY+iIuQI2YDRo0iKIvYubl5QkGdeXKlaVVq1bB6uf3z+2qq65yoE5OTnY19fu/hbLbtm3rdL3wwgslNzfX1VaoWAm/GDPQ9+KLL5batWs7aCf+Fuo9MWbS0tIEEwS0DhXr934xZlBDiF9mgOEmJ06cKNu3b3fbK2yxQl24qZKSEmnWrJlbCW3atClYrEQOyGv9+vVu5uzYsaOsXbs2eEwsv7dt2ybPPPOMA8qKFSui6IucFy5c6GYxdAWPoS9iLlmyxBUdVvLr1q0Lri9iYtuK1TxWfaipxPMO+Y6t6vjx4yUzM1PQ+TzGmNmyZYuLlZ2dLU8++aTrgh4yR/jG9nz16tVu4sfqD1qjpkPHRa49evSQbt26lR1gWJrivAR73JMnTwa9jh496gYVVkSPP/64YM8bOuaPP/4o33///W976127dgWPiZwQ9+WXX3arL4A7hr6Ii7MZrILeeOONKPoiJqCFouvbt6/s3r07ir4YTA8//LDTF2eMoesI/g8ePCivvfaaW1kvXbo0yjPFWerHH3/sdknjxo2TAwcOBM8VZ37ffvut28rdf//9zv7555+Dx0WuOEf9S2dgVapUcbP2mTNn/rDntP4FigB0x7K4qKjIHUZax/D9nT59WvDhQb9+/dwqDAexoV9nz56VU6dOCVZBWH5j9oqhL/IqLi4WbHWwQkAhxnjxU8hwKvNTSNW21DMwAkwFsrIIMCsl/9zP3r173QclLVu2dFu5P/+Xdn/Bp3Pz58+XunXryvLly6NMSgSYPj8CjN8D02owtLgCMxTTc0WAqSAEGAGm1WBoEWCGYnquCDAVhAAjwLQaDC0CzFBMzxUBpoIQYASYVoOhRYAZium5IsBUEAKMANNqMLQIMEMxPVcEmApCgBFgWg2GFgFmKKbnigBTQQgwAkyrwdAiwAzF9FwRYCoIAUaAaTUYWgSYoZieKwJMBSHACDCtBkOLADMU03NFgKkgBBgBptVgaBFghmJ6rggwFYQAI8C0GgwtAsxQTM8VAaaCEGAEmFaDoUWAGYrpuSLAVBACjADTajC0CDBDMT1XBJgKQoARYFoNhhYBZiim54oAU0EIMAJMq8HQIsAMxfRcEWAqCAFGgGk1GFoEmKGYnisCTAUhwAgwrQZDiwAzFNNzRYCpIAQYAabVYGgRYIZieq4IMBWEACPAtBoMLQLMUEzPFQGmghBgBJhWg6FFgBmK6bkiwFQQAowA02owtAgwQzE9VwSYCkKAEWBaDYYWAWYopueKAFNBSgUYWnkvWLBAfvnlF9cmCv0LQ11o9rp161bXt/Cpp54StKkKFSvhFwWAZqBouoquv2hyi16Rib+HeId/9MCcNGmSoO0XunTjPkLE8n2i4WqbNm3kzTffjKIv4m/YsEEKCgqkf//+gnZn/j2F+HnPnj0yatQoadGihaupEDF8n2jMjCbQderUcc1mYzxTNERG5/HGjRvLhAkTXLNi/76sfwYLvvvuO+nSpYsMGTLE2ehzah3n9/4wZtDHFDX0lxrbpqWlybBhw1y/O7SlD3m9/vrrrlt1/fr1pVevXjJ37tyg8ZAL+vjNmjXLQbN58+Yyffp0N7hD5gl4oDP2wIEDXbGjQzfuI2TMhO8xY8ZITk6Oe6Yx9EXc559/XvLy8lzD4hkzZkTJc9q0aa5RcXZ2tqupRP4h3+fMmSMPPvigoJs9OsvHeKYYM2PHjpWsrCwZMGCAzJ49O7i+WNBgnOTm5rqO69AaNR1SW/jH5JCfny/XXXedm/R17fUvq9QVGP4DIIaVGJrchrzw4FNTU+Xcc8+V5ORkVwgh48E38srIyJBy5crJhRdeKOnp6UFzTOSDuBdccIGcf/750fRFbOh63nnnySWXXBJFX8SsUKGCyxO5xtIXcZKSklwtoX4Tuod8r1ixopQvX17OOeccSUlJiTZmkB/GzMUXXyy4h5A5wjdqF3HwPGOPGehaVFQku3bt8vklpQLsD/+Kv6ACVIAK/A0VIMD+hg+Ft0QFqEDZFCDAyqYT/xUVoAJ/QwUIsL/hQ+EtUQEqUDYFCLCy6cR/RQWowN9QAQLsb/hQeEtUgAqUTYH/ByAX0e/WkTJhAAAAAElFTkSuQmCC[/img][br][br]Clare said she sees 100.[br]Tyler says he sees 1.[br]Mai says she sees [math]\frac{1}{100}[/math].[br]Who do you agree with?
In the diagram, the medium rectangle is made up of 10 small squares. The large square is made up of 10 medium rectangles.
Explain your reasoning.
Complete the table to explore patterns in the exponents when multiplying powers of 10. You may skip a single box in the table, but if you do, be prepared to explain why you skipped it.
If you chose to skip one entry in the table, which entry did you skip? Why?
Use your rule to write [math]10^4\cdot10^0[/math] with a single exponent.  What does this tell you about the value of [math]10^0[/math]?
The state of Georgia has roughly [math]10^{^7}[/math] human residents. Each human has roughly [math]10^{^{13}}[/math] bacteria cells in his or her digestive tract. How many bacteria cells are there in the digestive tracts of all the humans in Georgia?
There are four ways to make by multiplying powers of 10 with smaller, positive exponents.
[math]10^1\cdot10^1\cdot10^1\cdot10^1[/math][br][math]10^1\cdot10^{^1}\cdot10^2[/math][br][math]10^1\cdot10^3[/math][br][math]10^2\cdot10^2[/math][br][br](This list is complete if you don't pay attention to the order you write them in. For example, we are only counting [math]10^1\cdot10^3[/math] and [math]10^{^3}\cdot10^1[/math] once.)[br][br]How many ways are there to make [math]10^6[/math] by multiplying smaller powers of 10 together?
How about [math]10^7[/math]?
 How about [math]10^8[/math]?
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Information: IM 8.7.2 Lesson: Multiplying Powers of Ten