Question

How do you model a decimal using a fraction

Answer 1

You model a decimal using a fraction :

multiply the denominator and numerator by 10 for every number after the decimal point after we change the decimal in fractions with the denominator 1

Further explanation

Fraction numbers are known as numerators and denominators

On a number line, fractions are expressed in points that lie between two integers

The general form of fractions is

$\large {\boxed {\bold {\frac {a} {b}}}$

a = numerator

b = denominator

Decimal numbers are numbers in which there are commas or decimal points.

The value of each number in decimal numbers is based on a comparison of the number 10

In a decimal system, the numbers have the following consecutive values ​​(the place value of the digits in a number): hundred thousands, ten thousands, one thousands, hundreds, tens, ones, decimal points, tenths, hundredths, thousandths, ten thousandths, hundred thousandths

Between ones and tenth values ​​separated by commas (decimal points)

Decimal numbers can also be expressed as proper or mixed fractions

The position of each digit in decimal numbers is important.

Because the decimal number is based on the number 10, As we move left, each position is 10 times bigger, and As we move right, each position is 10 times smaller

On the left of the decimal point is a whole number

To convert a Decimal to a Fraction there are several steps:

• 1. Write down the decimal in fractions with the denominator 1
• 2. We multiply the denominator and numerator by 10 for every number after the decimal point.
• 3. Simplify the fraction if needed

Example:

$\displaystyle 0.459$

$\displaystyle = \frac{0.459}{1}$

$\displaystyle = \frac{459}{1000}$

$\displaystyle 0.75$

$\displaystyle = \frac{0.75}{1}$

$\displaystyle = \frac{75}{1000}$

$\displaystyle = \frac{3}{4}$

if there is a whole number part, set aside first, make changes to the fraction then return it at the end

$\displaystyle 3.25$

$\displaystyle = \frac{0.25}{1}$

$\displaystyle = \frac{25}{100}$

$\displaystyle = \frac{1}{4}$

$\displaystyle = 3\frac{1}{4}$

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Keywords: decimal, decimal point, fraction, convert a Decimal to a Fraction

Answer 2

Answer:

If we have to model a decimal using fraction , This is the way you should write

 $1.\rightarrow a.b_{1}=\frac{ab_{1}}{10\text{or}(10^1)}\\\\2.\rightarrow a.b_{1}b_{2}=\frac{ab_{1}b_{2}}{100\text{or}(10^2)}\\\\ 3.\rightarrow a.b_{1}b_{2}b_{3}=\frac{ab_{1}b_{2}b_{3}}{1000\text{or}(10^3)}\\\\............\\\\\text{General rule}\\\\n.\rightarrow a.b_{1}b_{2}b_{3}.......b_{n}=\frac{ab_{1}b_{2}b_{3}.....b_{n}}{1000.....0\text{or}(10^n)}$