Converting Decimals to Fractions
and Fraction to Decimals
Math 8
Learning Targets
• I will express a fraction as a decimal – terminating
and repeating.
• I will express a decimal as a fraction.
Vocabulary
• Terminating Decimal – A decimal number that has
digits that do not go on forever
• Repeating Decimal – A decimal number that has
digits that repeat forever.
Write a Fraction as a Decimal
a)
1
8
Divide, 1 ÷ 8 = 0.125
5
b)
12
Divide, 5 ÷ 12 = 0.41666 … = 0.416
Repeating Decimal
Express a Decimal as a Fraction
Terminating
Express a Decimal as a Fraction
Terminating
Express a Decimal as a Fraction
Terminating
Express a Decimal as a Fraction
Terminating
Express a Decimal as a Fraction
Terminating
Express a Decimal as a Fraction
Repeating
Convert 0.8888888 𝑡𝑜 𝑎 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛
Step 1 - Let x equal the repeating decimal your trying to convert.
𝑥 = 0.8888888
Step 2 – Examine the repeating decimal to find the repeating
digit(s).
Step 3 – Place the repeating digits(s) to the left of the decimal
point.
10𝑥 = 8.888888
Express a Decimal as a Fraction
Repeating
Convert 0.8888888 𝑡𝑜 𝑎 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛
Step 4 – Subtract the left side of the equations from the right.
10𝑥 − 𝑥 = 8.8888888 − 0.8888888
9x = 8
8
𝑥=
9
Write a Decimal as a Fraction
Repeating
Step 1, 𝑥 = 0.124124124
Step 2, Repeating 124
Step 3, Put repeating digits to left of decimal point
124.124124124
Write a Decimal as a Fraction
Repeating
𝐶𝑜𝑛𝑣𝑒𝑟𝑡 0.124124124 𝑡𝑜 𝑎 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛
Step 4, 1000𝑥 = 124.124124124
Step 5, Subtract left sides and right sides
1000𝑥 − 𝑥 = 124.124124124 − .124124124
999𝑥 = 124
124
𝑥=
999
Write a Decimal as a Fraction
Repeating
𝐶𝑜𝑛𝑣𝑒𝑟𝑡 1.16161616 𝑡𝑜 𝑎 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛
Step 1, 𝑥 = 1.16161616
Step 2, Repeating digits 16
Step 3, Put repeating digits to the left of the decimal
116.16161616
Write a Decimal as a Fraction
Repeating
𝐶𝑜𝑛𝑣𝑒𝑟𝑡 1.16161616 𝑡𝑜 𝑎 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛
Step 4, 100𝑥 = 116.16161616
Step 5, Subtract left sides and right sides
100𝑥 − 𝑥 = 116.16161616 − 1.16161616
99𝑥 = 115
115
16
𝑥=
=1
99
99