Question

Mrs. Herman asked the class to write an expanded form for 412.638. Nancy wrote the expanded form using fractions, and Charles wrote the expanded form using decimals. Write their responses.

Answer 1

Answer:

Mrs. Herman asked the class to write an expanded form for 412.638.

Nancy wrote the expanded form using fractions. Her response is like:

$(4\times100)+(1\times10)+(2\times1)+(6\times\frac{1}{10})+(3\times\frac{1}{100})+(8\times\frac{1}{1000} )$

Charles wrote the expanded form using decimals. His response is like:

$(4\times100)+(1\times10)+(2\times1)+(6\times0.1)+(3\times0.01)+(8\times0.001)$

Answer 2

The number 412.638 has six digits, three digits before decimal and three digits after the decimal.

Further explanation:

In number every digit  has a place value. Place value represent by a digit in a number on the basis of its place in the number defined by place value chart.

From place value chart of decimal numbers, expand the number 412.638 in fraction as follows:

$\begin{aligned}412.638&=4\times\left({\dfrac{{100}}{1}}\right)+1\times\left({\dfrac{{10}}{1}}\right)+2\times\left({\dfrac{1}{1}}\right)+6\times\left({\dfrac{1}{{10}}}\right)+3\times\left({\dfrac{1}{{100}}}\right)+8\times\left({\dfrac{1}{{1000}}}\right)\\&=\dfrac{{400}}{1}+\dfrac{{10}}{1}+\dfrac{2}{1}+\dfrac{3}{5}+\dfrac{3}{{100}}+\dfrac{1}{{125}}\\\end{aligned}$

Therefore, the expanded form for 412.638 in fractions is $\boxed{\dfrac{{400}}{1}+\dfrac{{10}}{1}+\dfrac{2}{1}+\dfrac{3}{5}+\dfrac{3}{{100}}+\dfrac{1}{{125}}}$.

So, Nancy write the number in the form $\boxed{\dfrac{{400}}{1}+\dfrac{{10}}{1}+\dfrac{2}{1}+\dfrac{3}{5}+\dfrac{3}{{100}}+\dfrac{1}{{125}}}$.

From place value chart of decimal numbers, expand the number 412.638 as follows:

$\begin{aligned}412.638&=4\times\left({100}\right)+1\times\left({10}\right)+2\times\left(1\right)+6\times\left({0.1}\right)+3\times\left({0.01}\right)+8\times\left({0.001}\right)\\&=400+10+2+0.6+0.03+0.008\\&=400.000+10.000+2.000+0.6.000+0.03.000+0.008.000\\\end{aligned}$

Therefore, the expanded form for 412.638 in decimals is $\boxed{400.000+10.000+2.000+0.600+0.030+0.008}$.

So, Charles write the number in the form $\boxed{400.000+10.000+2.000+0.600+0.030+0.008}$.

Thus, the expanded form for 412.638 in fractions is $\boxed{\dfrac{{400}}{1}+\dfrac{{10}}{1}+\dfrac{2}{1}+\dfrac{1}{6}+\dfrac{1}{{30}}+\dfrac{1}{{800}}}$ and in decimals is $\boxed{400.000+10.000+2.000+0.600+0.030+0.008}$.

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Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Decimal system

Keywords: expanded form, fraction form, decimal form, expand, place value chart, Charles, Nancy, number.