Mathematics
Grade 6
15 min
Convert between decimals and fractions
Convert between decimals and fractions
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify decimals and fractions as different representations of rational numbers.
Convert terminating decimals to fractions in simplest form.
Convert fractions to terminating decimals using division.
Understand the role of place value in decimals when converting them to fractions.
Simplify fractions after converting from decimals.
Recognize when a fraction will result in a terminating decimal.
Ever wonder how a recipe calls for 'half a cup' (fraction) but your measuring spoon shows '0.5 cups' (decimal)? 🤔 They're the same amount!
In this lesson, you'll learn how to switch back and forth between decimals and fractions. This skill is super useful for understanding numbers better and solving everyday math problems, from cookin...
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Key Concepts & Vocabulary
TermDefinitionExample
DecimalA way to represent numbers that are not whole, using a decimal point to separate the whole part from the fractional part.0.75 (seventy-five hundredths)
FractionA way to represent a part of a whole, written as a ratio of two integers (numerator over denominator).$ rac{3}{4}$ (three-fourths)
NumeratorThe top number in a fraction, indicating how many parts of the whole are being considered.In $ rac{3}{4}$, 3 is the numerator.
DenominatorThe bottom number in a fraction, indicating the total number of equal parts the whole is divided into.In $ rac{3}{4}$, 4 is the denominator.
Simplest Form (of a fraction)A fraction where the numerator and denominator have no common factors other than 1.$ rac{1}{2}$ is the simplest form of $ rac{2}{4}$.
Place Value (Decimals)The va...
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Core Formulas
Converting Decimals to Fractions
$0.abc... = \frac{abc...}{10^n}$ where $n$ is the number of decimal places.
Write the decimal number (without the decimal point) as the numerator. For the denominator, write a 1 followed by as many zeros as there are digits after the decimal point. Then simplify the fraction.
Converting Fractions to Decimals
$\frac{a}{b} = a \div b$
Divide the numerator by the denominator. The result will be the decimal equivalent.
Simplifying Fractions
$\frac{a}{b} = \frac{a \div \text{GCF}(a,b)}{b \div \text{GCF}(a,b)}$
Find the greatest common factor (GCF) of the numerator and the denominator, then divide both by the GCF to get the fraction in its simplest form.
5 more steps in this tutorial
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Sign Up Free to ContinueSample Practice Questions
Challenging
If you convert the decimal 1.45 to a mixed number and simplify the fractional part, what is the numerator of the simplified fraction?
A.45
B.9
C.20
D.29
Challenging
Which of the following fractions will result in a terminating decimal?
A.$\frac{7}{20}$
B.$\frac{2}{3}$
C.$\frac{4}{7}$
D.$\frac{5}{12}$
Challenging
A student tried to convert 0.05 to a fraction and wrote $\frac{5}{10}$. What was their mistake?
A.They should have written $\frac{1}{20}$.
B.They used the wrong numerator.
C.They used the wrong place value for the denominator.
D.They forgot to divide 10 by 5.
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