Sage-Tips

How do you show that a decimal is infinite?

To show an infinite decimal, we write “…” at the end. This is also good for when you get bored writing all the digits of a lengthy finite decimal, or when your pen is running out of ink. Another way to write an infinite decimal with a repeating pattern is to draw a bar over the part that repeats.

How do you turn a fraction into a decimal and determine if it is repeating or terminating?

Just divide the numerator by the denominator . If you end up with a remainder of 0 , then you have a terminating decimal. Otherwise, the remainders will begin to repeat after some point, and you have a repeating decimal.

Why can you use fractions to represent a decimal number?

A fraction where the denominator (the bottom number) is a power of ten (such as 10, 100, 1000, etc). You can write decimal fractions with a decimal point (and no denominator), which make it easier to do calculations like addition and multiplication on fractions.

What do you call a number with infinite decimals?

A repeating decimal, also called a recurring decimal, is a number whose decimal representation eventually becomes periodic (i.e., the same sequence of digits repeats indefinitely).

Can infinite decimals be written as fractions?

A repeating decimal can always be written as a fraction using algebraic methods that are beyond the scope of this article. However, it is important to recognize that any decimal with one or more digits that repeats forever, for example …

How do you tell if a decimal can be written as a fraction?

Decimals can be written in fraction form. To convert a decimal to a fraction, place the decimal number over its place value. For example, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction, 6/10.

How will you write 0.444 in a fraction form?

4/9
For example, using this method allows us to find that 0.444… = 4/9, 0.888… = 8/9, and 0.999… = 9/9—which means that it’s equal to 1.

How do I write fractions as decimals?

The line in a fraction that separates the numerator and denominator can be rewritten using the division symbol. So, to convert a fraction to a decimal, divide the numerator by the denominator. If required, you can use a calculator to do this. This will give us our answer as a decimal.

How do you write fractions as a decimal?

To write a fraction as a decimal, divide the numerator by the denominator. When writing a fraction as a decimal, your result is a terminating or repeating decimal. A repeating decimal repeats a pattern of one or more digits.

Can every infinite repeating decimal be expressed as a fraction?

Every infinite repeating decimal can be expressed as a fraction. Find the fraction represented by the repeating decimal . Let n stand for or 0.77777 … So 10 n stands for or 7.77777 … 10 n and n have the same fractional part, so their difference is an integer.

What do you know about decimal expansion?

• Students know that every number has a decimal expansion (i.e., is equal to a finite or infinite decimal). • Students know that when a fraction has a denominator that is the product of 2’s and/or 5’s, it has a finite decimal expansion because the fraction can then be written in an equivalent form with a denominator that is a power of 10.

What does it mean if an equation has an infinite number?

It means that if the system of equations has an infinite number of solution, then the system is said to be consistent. As an example, consider the following two lines. These two lines are exactly the same line. If you multiply line 1 by 5, you get the line 2.

Is 3/6 a terminating or non-terminating decimal?

Here, the quotient is 0.5 and the remainder is 0. Rational number 3/6 results in a terminating decimal. Example: Express 5/13 in decimal form. Here, the quotient is 0.384615384 and the remainder is not zero. Notice that the number…384 after the decimal is repeating. Hence, 5/13 gives us a non-terminating recurring decimal expansion.