Getting to the Point

How long does it take a speaker to get to the point?
OBJECTIVE: To learn how to convert fractions to decimals
[br]In previous lessons, you learned how to work with fractions.[br][br][i][color=#0000ff]Wearing Uniforms: [/color][/i][url=https://www.geogebra.org/m/ceyu3wpa]https://www.geogebra.org/m/ceyu3wpa[br][/url][i][color=#0000ff]Mixing 'Em Up: [/color][/i][url=https://www.geogebra.org/m/hzx95nwa]https://www.geogebra.org/m/hzx95nwa[br][/url][color=#0000ff][i]Reducing, Reusing, Recycling: [/i][/color][url=https://www.geogebra.org/m/gcxtdncg]https://www.geogebra.org/m/gcxtdncg[br][/url][i][color=#0000ff]Doing the Flip:[/color] [/i][url=https://www.geogebra.org/m/pqym69rc]https://www.geogebra.org/m/pqym69rc[/url][br][br]In this lesson, you're going to learn how to convert [color=#0000ff]FRACTIONS[/color] to [color=#0000ff]DECIMALS[/color] and subsequently perform operations on decimals. Fractions and decimals are simply two ways of expressing the relationship of a part to the whole.[br][br]The applet below will show you graphically how fractions and decimals are related using a bar model. Interact with the applet for a few minutes. Move the sliders to generate fractions and observe how they get converted to decimals. The arithmetic process will be discussed later.
Converting fractions to decimals
HOW TO CONVERT FRACTIONS TO DECIMALS
[br]A fraction is simply an implied division with the [color=#0000ff]FRACTION BAR[/color] (also called [color=#0000ff]DIVISION BAR[/color]) functioning as the [color=#0000ff]DIVISION BOX[/color] in long division. So to convert a fraction into a decimal, just do the division and place the [color=#0000ff]DECIMAL POINT[/color] in its proper place.[br][br]Examples: [br][br] [img]data:image/png;base64,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[/img][br][br][img]data:image/png;base64,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[/img][br][br][img]data:image/png;base64,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[/img][br][br]One convenient method to change fractions to decimals without doing long division is to come up with an [color=#0000ff]EQUIVALENT FRACTION[/color] whose denominator is a power of 10 and then move the decimal point of the numerator to the left the same number of times as there are zeros in the denominator. The denominator is then removed. Of course, this method will only work for fractions whose denominator is a factor of powers of 10.[br][br]Examples:[br][br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIwAAAA5CAYAAADkx8P4AAAJW0lEQVR4Ae1cX6gjVxnP3t1urX9AK+hWLesKFqU2lFoEfWr2pYLWQSuCkAefYqEPDa4FU0G6kT5kEdmsDxvEy2i9odYUNH1Jl26URoqzQpTmwVSJ9BY3WzvK3N5h9w5s7vYnZ/5lMjnnzJmbmWRyOYEhmTPfmfOdb37zne98f5KD/EgJxJBALgatJJUSgASMBEEsCUjAxBKXJJaAkRiIJQEJmFjiksQSMBIDsSQgARNLXJJYGDATy5LSkhKI3lbvjodonSshl8uhqA6XIzKrDyW3YY9Jxg0epdZoOTx4o2SJF4+nFX4zNYz1r/bcQ1Pq/eWwavVRzB2dAYoHmnrfWA4P3ihZ4sXjaYXfTMBM3uigmC9AURTkc0fsh7cswFhD1R1PW6FonKGzxMvKhQFEL0mEyUGjGAswk+02jhzJoz2i2z3moImNjQI64wlVBuag4YzXGFCvL7MxS7wsc96ssZgaJtghLmBgDlDOHXNAsT0LGnPYtMFwLF/F0Ho3OIz/23IBk8srKFdqaLY16Axav1NKP7LES0pTjHXbdABDWJgBjaNJzGHLXt4IWEYTOlhI10FDsUHl2S3km2gs9a96rMklQZwlXpKYz6L3SA8whDOzj1LuKG47WsQLbRWF3AZssERoC3M8Qr+v4aWWikqx4IPn+LESUystKghW/yzxwuJxme3pAobMxJxukd9zvMLVLKyJ65pj0xBNs/RdUoipLPESYm0pp6kDxho5yxB52ETTdBmGLn+2FlTlhK1pVg0YIEu88KWWxtVUAWO5NkuuUMNgW7MN4aMbSnzQ7PRsn5C983qDvrNKQzjUe2aJFyqD6TYKAWbob6vFt7nE8Uf8Nxv5ytTuMBybJg5ojO0eKoU7be1ClrTtdOXBvXtmeJlYME3TPpb9+nAAY0Jrq6iWi77jjrzhxJF3vsN/bJNxx+5DHvDc1tnQbEOYBZpRt4WGqqJeq6B4+oO+wevQz27RuU83gYtZ4sWZjoluvezLhCzzRC7qlXH0bBMKcbABwxkg0uNraCgrFQxMxtZZ76GsVKnX+6EtNQFp6WwTQ+NWtFASpsgSL4ABtfgJHyzFUglK/g7/vNqNAE1CIQ42YBIWfpzbmfoY4/EYum5g2So3zGdWeBm1HM1CNErHd4bqUEt5GzS331bmLtdJhTgyCZjwQ5PnOs4VPmwDo9IJaRJT84PE6sBkiiqpEIcEDFPEGbrg+rKIdtHmlnkTDeWjNphqPbYnPKkQxyEBjI52o456nXfUcGFLw3LN5iDoDs6jpx2OnK6Dltzh2VoFTvpJUiGOwwEYa4hy/n3I5fPIsw6SolFUwVbawYebwu8FePQAk1MaVP5FgsNJhTiogDlz5gxEDyuUurm7uyvcV3SMMN2FCxcSe6LXrl1Lhd+LFy8mxmMUYLpVJ95WjpGNeNAQBxUwzWYTosfNmzdnBLO3tyfcV3SMMN2lS5dmxiQnJOeYgJd7TOb3XDs7O6nwe/ny5cR49HY4ZCc0H+U3UHcN4np/d25MdsPBQhxUwLAHyegVq29Hwokji3d84A66DbCUWS3CY8CHog5DVpjedTzqGwV09fkXgjm3A4Y4DgdgYGHY66Lb66HHPLro9bdX6NdZhEcLTc9pVwjmEuloFD/uvCTFpmvQT2DoOgyLDR5eiGP/5g2Y5g3sM5B2SADDmN0havYyFW0NamciTkMnTtjEAYhn72wUpgayeIjDwpXnN7G5uYlX3gxpMleWEjBrBCrjtZbvpPOXXqUCLbAUmVtP2honCBhv2+31YYZbfrWJK79IADATy4mMcrTcGok9mlXRoj3LjRibSxWMBd0Om5DwCcUrU/kejLs/Av2VP81MVCjE8eMfYf/s0/jfzgGXpFFPRem0E6vw0Fmqd6i+gBnuFj3hBD7TLGQTLdozRx2UCx+aMbCVShMHyg1bVFbh/g/cC3zyBFD6TvhK9PkPzgC1Z7h0zCWp7+bAEKAoxdnIqNJIuaAtsCvwgOp9p5FxF6doz+g7NVM2P6eLKJemCevH8zVuAJD7JJK4+M/XgVMfA06eAD51F/BfdqiAOtwTjwE/O0+95DXSARN4wxuaN6iFTsVxELFc1N5NF/32/A5KfTmFbMJFe5ORnTVov0S1rh9m0AMgKrf5uUKLyobb/1nV0S6fvtsBza9/ySWfu/jNrwG/fW6uOdhAB4ypOX4NRfWFQjp5AaygQRW8mfd7nQvZeG52vVezl6H33l7FVW+y7rdWdzWNssLww43rwN/6wH33AL/ZAsh5nM+D9wF/4b+kdMDAQKdencus225X5ixwKj8zNUmz2zNve5jVQjYeYPouKAq1eaF621myLHk6mSqbZTR+46vAC8/HG4mAiyxlOp97BmAoYwXUsZDanQGN6yNYg0I2NmDMaeWCRtmdcFMQKPJMs+mpJ4GnfxhvhFd7wIOfi+wjCBgLrbK7W1Ia1BA7daQ1LGTjAcbLO6Ea3q6hTs9ZoUonvcYXfwd8uRDv/j89Bzz+3cg+AoCZwIuGkspDZp4ua6g1K2QTAUyDltmmd227jx4gZAknpXayrJy6C3j7bfEBHn0EaD4bSR8BmAm6NceYC7qfI+8aIFi3QjYeYLx4Di2NwNDqYvZdQDap/iQ7ns2fiw3x1jVnG/6ftyLpOYAx0Xa30aRisXcAr9Q6FrKxATP925OcH+ibyrfn5qTkq91p4yp/PbcFPPyQGAfnfwIUvyVEywCMjqabjW7/j8vIgGUaMIzpEeUNX9dCNl7RnucfIn6Ys4HarGAy0lY4/UDoMaRAtHcD+Py9wMsv8W9+/Tpw/2eBP8zn79A6UgFjDhz16nlXad+8/NH1K2QTLdoz0Syd9EMCSqmMStn5syUio0Ktu8L0CcrjJUvSQ18ErD3KRbfpmbMA2YYLfqiAwWSEp/Lv9wUTBgyJdvJKGrBuhWwBz3Z4rvNFewZa1SlIPPpKU8sWWAgA9veBr38F+P4TwLuUosLuy8BnTgH/EP+zSzpgBNGWFplQZDWtwQXvaxk6xrpuR46NiP+7EbxlOmRX/w184X6g/DjwzjvOGLduAcTGIWB58fexxs0kYGLNQBJHS2B8Ffj2o8A9J4FHHnYcdF96APhjfANdAiZa3IeH4vW/Oxrlz68CoeR90UlKwIhKStLZEpCAkUCIJQEJmFjiksQSMBIDsSQgARNLXJJYAkZiIJYEJGBiiUsS/x8GPLzFlo47fwAAAABJRU5ErkJggg==[/img][br][br][img]data:image/png;base64,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[/img][br][br][img]data:image/png;base64,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[/img][br][br]One more thing, dividing the numerator by the denominator doesn't always end up as a [color=#0000ff]TERMINATING DECIMAL [/color](one that ends). Sometimes, you'll get a [color=#0000ff]REPEATING DECIMAL[/color] (one that repeats a certain number of digits). In the latter case, a horizontal bar is placed over the top of the digits that repeat.[br][br]Examples:[br][br][img]data:image/png;base64,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[/img][br][br][img]data:image/png;base64,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[/img][br][br][img]data:image/png;base64,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[/img]
Use the applet below for practice.
Below is a set of problems that require you to convert fractions to decimals.
Converting Fractions to Decimals
ANSWER BOX:
[br]Check your answers below.
Converting Fractions to Decimals_Answer Key
In this lesson, you learned how to convert fractions to decimals.
In future lessons, you'll do more work on fractions and decimals. Hope you had FUN today.

Information: Getting to the Point