🔢 MathGrade 4Lesson 22
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Relate Fractions to Decimals

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Learning Objectives

  • 1Convert fractions with denominators of 10 or 100 to decimals
  • 2Convert decimals to fractions with denominators of 10 or 100
  • 3Identify common fraction-decimal equivalents (1/2, 1/4, 3/4)
  • 4Place fractions and their decimal equivalents at the same position on a number line
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Mini Lesson

Fractions and decimals are two ways to write the same value. A fraction shows how many equal parts out of a whole; a decimal uses the base-10 place-value system to show the same amount. They name the same point on a number line.

Fractions with Denominator 10 or 100

  • A fraction whose denominator is 10 converts directly to one decimal place: 3/10 = 0.3.
  • A fraction whose denominator is 100 converts directly to two decimal places: 47/100 = 0.47.
  • The numerator becomes the digits after the decimal point.

Key Equivalents to Memorize

  • 1/2 = 0.5 (one half)
  • 1/4 = 0.25 (one quarter)
  • 3/4 = 0.75 (three quarters)
  • 1/5 = 0.2
  • 1/10 = 0.1

Converting Other Fractions

  • Find an equivalent fraction with denominator 10 or 100, then read it as a decimal.
  • 1/4 = 25/100 = 0.25 (multiply numerator and denominator by 25).
  • 1/5 = 2/10 = 0.2 (multiply numerator and denominator by 2).
  • 3/5 = 6/10 = 0.6 (multiply both by 2).
Reference table of key fraction-decimal equivalentsKey Fraction-Decimal PairsFractionDecimal1/20.51/40.253/40.751/50.21/100.1
Number line from 0 to 1 showing fractions and decimals at the same pointsFractions and Decimals on a Number Line001/40.251/20.53/40.7511Fraction and decimal = same point on the line
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Tip: to convert a fraction to a decimal, find an equivalent fraction with 10 or 100 as the denominator, then write the numerator after the decimal point.

Vocabulary
Fraction
A number that shows equal parts of a whole or a sete.g. 1/4 is a fraction.
Decimal
A number that uses a decimal point to show parts of a wholee.g. 0.25 is a decimal.
Tenths
The place one step to the right of the decimal pointe.g. 0.3 means three tenths.
Hundredths
The place two steps to the right of the decimal pointe.g. 0.27 means twenty-seven hundredths.
Equivalent
Of equal value — a fraction and a decimal can be equivalente.g. 1/4 and 0.25 are equivalent.
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← Lesson 21: Introduce Decimals: Tenths and HundredthsLesson 23: Round and Compare Decimals →