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Ch7 Notes (F09) - Section 7-1 Introduction to Decimals...

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1 Section 7-1 Introduction to Decimals Decimals are an alternative was of representing fractions using our base-10 system. Connecting Decimals and Integers : Decimals and integers are both base-10 place value systems. The value of each digit depends on its place, and the value of each place (to the right) is one-tenth the value of the previous place. thousands hundreds tens ones tenths hundredths thousandths 10 3 10 2 10 1 10 0 10 1 10 2 10 3 1,000 100 10 1 0.1 0.01 0.001 Examples : Using the Base-10 blocks, if we let the Flat = 1, then how would you represent: a) 2.3 b) 1.25 c) 3.01 Examples : Use words to describe: a) 5.45 b) 4.06 c) 0.302 Examples : Write the following decimals in expanded form with exponents: a) 2.41 b) 25.0457
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2 Connecting Decimals and Fractions By using the concept of place value, decimals can be translated into fractions. Examples : Convert the following decimals to fractions a) 0.35 b) 2.25 c) 4.501 Examples : Convert the following fractions to decimals a) 63 100 b) 315 10,000 c) 7 20 d) 27 250 When fractions are converted to decimals, some will terminate and some will not. What causes a fraction to terminate? A fraction will only terminate if the denominator can be written as a _____________________.
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3 Theorem : A rational number a b in simplest form can be written as a terminating decimal if and only if the prime factorization of the denominator contains no primes other than 2 or 5.
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