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.

Respuesta :

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:

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

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

[tex](4\times100)+(1\times10)+(2\times1)+(6\times0.1)+(3\times0.01)+(8\times0.001)[/tex]

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:

[tex]\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}[/tex]

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

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

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

[tex]\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}[/tex]

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

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

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

Learn more:

1. Write an algebraic expression for the following word phrase the quotient of r and 12 https://brainly.com/question/1600376

2. 9 ten thousands ÷ 10 in unit form https://brainly.com/question/4786449

3. What is the value of the digit 4 in the number 84 230 https://brainly.com/question/106975

4. Ten hundredths in standard form https://brainly.com/question/228852

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Decimal system

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

ACCESS MORE
EDU ACCESS