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QuestionConvert the following expressions to decimals: a. (3×10)+(5×1)+(2×110)+(7×1100)+(6×11000)(3 \times 10)+(5 \times 1)+(2 \times \frac{1}{10})+(7 \times \frac{1}{100})+(6 \times \frac{1}{1000}) b. (9×100)+(2×10)+(3×0.1)+(7×0.001)(9 \times 100)+(2 \times 10)+(3 \times 0.1)+(7 \times 0.001) c. (5×1,000)+(4×100)+(8×1)+(6×1100)+(5×11000)(5 \times 1,000)+(4 \times 100)+(8 \times 1)+(6 \times \frac{1}{100})+(5 \times \frac{1}{1000})

Studdy Solution

STEP 1

Assumptions1. We are given expressions that represent decimal numbers in expanded form. . Each term in the expression represents a digit in a specific place value of the decimal number.
3. We need to convert each expression into a standard decimal form.

STEP 2

Let's start with the first expression(×10)+(5×1)+(2×110)+(7×1100)+(6×11000) ( \times10)+(5 \times1)+\left(2 \times \frac{1}{10}\right)+\left(7 \times \frac{1}{100}\right)+\left(6 \times \frac{1}{1000}\right)

STEP 3

Calculate each term in the expression.
=30+5+0.2+0.07+0.006 =30+5+0.2+0.07+0.006

STEP 4

Add up all the terms to get the decimal number.
=30++0.2+0.07+0.006=35.276 =30++0.2+0.07+0.006 =35.276

STEP 5

Now, let's move on to the second expression(9×100)+(2×10)+(3×0.1)+(7×0.001) (9 \times100)+(2 \times10)+(3 \times0.1)+(7 \times0.001)

STEP 6

Calculate each term in the expression.
=900+20+0.3+0.007 =900+20+0.3+0.007

STEP 7

Add up all the terms to get the decimal number.
=900+20+0.3+0.007=920.307 =900+20+0.3+0.007 =920.307

STEP 8

Finally, let's solve the third expression(5×1,000)+(4×100)+(8×1)+(6×1100)+(5×11000) (5 \times1,000)+(4 \times100)+(8 \times1)+\left(6 \times \frac{1}{100}\right)+\left(5 \times \frac{1}{1000}\right)

STEP 9

Calculate each term in the expression.
=500+400+8+.06+.005 =500+400+8+.06+.005

STEP 10

Add up all the terms to get the decimal number.
=5000+400+8+0.06+0.005=5408.065 =5000+400+8+0.06+0.005 =5408.065 So, the decimal forms of the given expressions area.35.276b.920.307c.5408.065

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