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GenaCL600 [577]
3 years ago
6

Diane wanted to write 6.463 using expanded notation she wrote the expression below the expression is 3 * 1 + 6 * 1 + 100 + 4 * 1

+ 1000 + 6 * 1 if Diane is correct explain the process you use if Diane is not correct explain that Diane might have been thinking when she made her mistake
Mathematics
1 answer:
natima [27]3 years ago
7 0

Answer:

Diane is incorrect. She should get either

6*1 + 4*\frac{1}{10} + 6*\frac{1}{100} + 3*\frac{1}{1000}

or

6*1 + 4*0.1 + 6*0.01 + 3*0.001

both represent the same idea, just in different formats

==================================

Explanation:

The first 6 is in the units or ones place value. We multiply 6 by 1.

The 4 is in the tenths place. We multiply it by \frac{1}{10} or 0.1

The second 6 is in the hundredths place. We multiply it by \frac{1}{100} or 0.01

The 3 is in the thousandths place. We multiply it by \frac{1}{1000} or 0.001

All of those products are then added up to form the original number given

6.463 = 6*1 + 4*\frac{1}{10} + 6*\frac{1}{100} + 3*\frac{1}{1000}

6.463 = 6*1 + 4*0.1 + 6*0.01 + 3*0.001

6.463 = 6 + 0.4 + 0.06 + 0.003

It might help to line up the terms like this

\begin{array}{ccc ccc}6.463 \to & 6 & . & 4 & 6 & 3\\\        & 6 & \ & 0.4 & 0.06 & 0.003\\\        & 6*1 & \ & 4*0.1 & 6*0.01 & 3*0.001\\\        & 6*1 & \ & 4*\frac{1}{10} & 6*\frac{1}{100} & 3*\frac{1}{1000}\\\end{array}

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