Which expression equals 0.867 in expanded form?

Which expression equals 0.867 in expanded form?

• A. 8/100 + 6/1000 + 7/10000
• B. 0.86 + 0.007
• C. 8/10 + 6/100 + 7/1000
• D. 800/1000 + 60/1000 + 7/1000

Answer: (C)

Understanding the place-value decomposition of decimals: each digit after the decimal represents a fraction whose denominator is a power of ten, based on its position. For 0.867, the 8 is in the tenths place, so it contributes 8/10. The 6 is in the hundredths place, contributing 6/100. The 7 is in the thousandths place, contributing 7/1000. Adding them gives 8/10 + 6/100 + 7/1000 = 0.867. This shows each digit’s value clearly by its place. The other forms either misplace a digit’s place value (for example, using 8/100 for the first term), lump parts together in a way that hides the separate place-value contributions (such as 0.86 + 0.007), or use a different breakdown that isn’t the standard place-value representation (though they may still sum to the same number). The expression that matches the decimal exactly in expanded form is 8/10 + 6/100 + 7/1000.

Understanding the place-value decomposition of decimals: each digit after the decimal represents a fraction whose denominator is a power of ten, based on its position.

For 0.867, the 8 is in the tenths place, so it contributes 8/10. The 6 is in the hundredths place, contributing 6/100. The 7 is in the thousandths place, contributing 7/1000. Adding them gives 8/10 + 6/100 + 7/1000 = 0.867. This shows each digit’s value clearly by its place.

The other forms either misplace a digit’s place value (for example, using 8/100 for the first term), lump parts together in a way that hides the separate place-value contributions (such as 0.86 + 0.007), or use a different breakdown that isn’t the standard place-value representation (though they may still sum to the same number). The expression that matches the decimal exactly in expanded form is 8/10 + 6/100 + 7/1000.