Conversion of Decimal 0.125 to a Simplified Ratio

$Math Problem$

Mathematics Grade 6

Question Content

Convert 0.125 to a ratio

Correct Answer

1:8

Detailed Solution Steps

1
Step 1: Rewrite 0.125 as a fraction. 0.125 has three decimal places, so it is equal to 125/1000.
2
Step 2: Simplify the fraction. Divide both numerator and denominator by their greatest common divisor, which is 125. 125÷125=1, 1000÷125=8, so the simplified fraction is 1/8.
3
Step 3: Convert the simplified fraction to a ratio, so 1/8 = 1:8.

Knowledge Points Involved

Decimal to Fraction Conversion

Decimals can be converted to fractions by using the place value of the last digit. For a decimal with one decimal place, the denominator is 10; two decimal places use denominator 100, etc. This is used to transform decimal values into fractional form for further operations like ratio conversion.

Fraction Simplification

A fraction is simplified by dividing both the numerator and denominator by their greatest common divisor (GCD), the largest number that divides both evenly. This reduces the fraction to its lowest terms for clear ratio representation.

Fraction to Ratio Conversion

A fraction a/b can be directly converted to the ratio a:b, where a is the antecedent (first term) and b is the consequent (second term) of the ratio. This works because ratios represent the same proportional relationship as fractions.

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