You can write the ratio between the two numbers 5 and also 7 together 5:7 or together 5/7. If girlfriend think the second kind looks prefer a fraction, you"re right. It"s likewise a reasonable number, since it"s a quotient, or ratio, of totality numbers. In this context, the words "ratio" and "rational" space related; a reasonable number is any type of number that can be written as a quotient of totality numbers. Reasonable numbers have the right to be written in decimal form, however not every decimal numbers room rational. A number is rational only if you can write it as a quotient of entirety numbers. The square root of 2 and also pi (π) are two instances of numbers the don"t satisfy this condition, so they room irrational numbers. Quotients through zero in the denominator are additionally irrational.

You are watching: Express the repeating decimal number as a quotient of two integers.

TL;DR (Too Long; Didn"t Read)

To express a decimal as a quotient of whole numbers, division by a strength of ten equal to the variety of decimal places.

The number 5 is a rational number, so friend must be able to express it as a quotient, and also you can. Dividing any number by 1 provides you the initial number, so to express one integer choose 5 together a quotient, you simply write 5/1. The same is true for negative numbers: −5 = −5/1.

Decimals are simply another means to compose fractions. A single decimal place tells friend to division the number through 10, therefore 0.5 is the exact same as 5/10. Two locations tells friend to division by 100, three areas tells you to division by 1,000 and so on. You divide by 10 come the power of the variety of digits to the best of the decimal point.

Mixed number consisting of one integer and decimal are likewise rational due to the fact that you deserve to express them as a fraction. For example, to express 5.36 as a fraction:

You"d main point the totality number and also the denominator, add them come the numerator and then usage that an outcome as the molecule of the new fraction:

Some decimal consist of an infinite variety of repeating integers, such as 0.33333... Or 2.135135135.... This numbers appear irrational, yet they aren"t, since it is possible to compose them as quotients of totality numbers. To execute this, you divide the repeating wire of number by one equally lengthy string that 9s.

See more: Jorge Wants To Write The Fraction As A Sum Of Unit Fractions ?

The number 2.135135135... Has actually three repeating digits: 135. Divide 135 by a cable of three 9s to gain 135/999 and also multiply that fraction by 2, i beg your pardon is the number to the left the the decimal point. Utilizing the ahead procedure to incorporate a totality number and also fraction, friend get:

\beginaligned 2 × \frac135999 &= (2 × 999) + 135 \\ \,\\ &= 1998 + 135 \\ \,\\ &= \frac2133999 \endaligned

Chris Deziel holds a Bachelor's level in physics and also a Master's degree in Humanities, He has taught science, math and also English in ~ the college level, both in his indigenous Canada and also in Japan. He started writing digital in 2010, offering info in scientific, cultural and helpful topics. His writing covers science, math and home improvement and design, as well as religion and also the oriental healing arts.