Decoding 1.58 as a Fraction: A Step-by-Step Guide
The decimal 1.58 might seem simple, but converting it to a fraction requires understanding place value and a bit of mathematical manipulation. This guide will walk you through the process, explaining each step clearly so you can confidently tackle similar conversions.
Understanding Decimal Places
Before diving into the conversion, let's refresh our understanding of decimal places. The number 1.58 has:
- 1: Represents the ones place (a whole number).
- 5: Represents the tenths place (5/10).
- 8: Represents the hundredths place (8/100).
Converting to a Fraction
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Write the decimal as a fraction with a denominator of 1:
1.58 = 1.58/1
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Multiply both the numerator and the denominator by 100 to eliminate the decimal point:
This step is crucial because we have two decimal places (tenths and hundredths). Multiplying by 100 (10²) moves the decimal point two places to the right.
(1.58 x 100) / (1 x 100) = 158/100
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Simplify the fraction:
This means finding the greatest common divisor (GCD) of both the numerator (158) and the denominator (100) and dividing both by it. The GCD of 158 and 100 is 2.
158/2 = 79 100/2 = 50
Therefore, the simplified fraction is 79/50.
Therefore, 1.58 as a fraction is 79/50.
Checking your work: You can always verify your answer by dividing the numerator (79) by the denominator (50). The result should be 1.58.
Conclusion:
Converting decimals to fractions involves understanding place value and using appropriate multiplication to eliminate the decimal point. Remember to always simplify the fraction to its lowest terms for the most accurate representation. This straightforward process can be applied to any decimal number you want to convert to a fraction.
