Decimal Fractions

Terminating Decimals and Repeating Decimals

Writing Decimal Fractions

To write eight-tenths using decimal place value, the digit 8 is placed in the tenths' column. When we transfer the value out of the table, we need to include the decimal point. For better clarity and readability, when there are no whole number values, it is best to put a zero in front of the decimal point to indicate that there are no whole number values.

Note that we inserted a zero in the numeral where the table has an empty position since this simply says that position has no value. When we read decimal fractions (decimals) out loud or write them in words, the word and   is placed where the decimal point occurs. In the table above, twenty and sixteen thousandths is an example of this.

Example: Write 127.836 in words, expanded fraction form, expanded decimal form and expanded exponential form.

words:	one hundred twenty-seven and eight hundred thirty-six thousandths
fraction expanded form:
decimal expanded form:	127.836 = 1 · 100 + 2 · 10 + 7 · 1 + 8 · 0.1 + 3 · 0.01 + 6 · 0.001
exponential expanded form:	127.836 = 1 · 102 + 2 · 101 + 7 · 100 + 8 · 10–1 + 3 · 10–2 + 6 · 10–3

Note that 0.500 = 0.50 = 0.5, which follows from simplifying common fractions . The digit five remains in the tenths' column so these values are all equal to five-tenths. The extra zeros need not be written when writing decimals (decimal fractions) unless a person is working with problems where significant digits (Significant figures - Wikipedia, the free encyclopedia) need to be expressed, such has in scientific studies.

Self-Check Problem

Write 305.0026 in words, expanded fraction from, expanded decimal form, and expanded exponential form.

words	Solution
fraction expanded form:	Solution
decimal expanded form:	Solution
exponential expanded form:	Solution

 

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