Question

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

Answer 1

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

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