In the realm of mathematics, the concept of five and nine tenths in standard form holds a prominent place. This article delves into the intricacies of this topic, providing a comprehensive understanding of its significance and applications.
Standard form, also known as decimal form, is a widely used method of representing numbers. It involves expressing a number as a whole number followed by a decimal point and its fractional part. In the case of five and nine tenths, the standard form is 5.9.
Five and Nine Tenths in Standard Form
The number five and nine tenths can be represented in standard form as 5.9. Standard form is a way of writing numbers that uses a decimal point to separate the whole number part from the fractional part. In this case, 5 is the whole number part and 9 is the fractional part.
Decimal Form
A decimal representation of a number is a way of writing a number using a decimal point. The decimal point separates the whole number part of the number from the fractional part. For example, the decimal representation of the number five and nine tenths is 5.9.
- The digits to the left of the decimal point represent the whole number part of the number.
- The digits to the right of the decimal point represent the fractional part of the number.
The placement of the decimal point is important. If the decimal point is moved to the left, the value of the number will increase. If the decimal point is moved to the right, the value of the number will decrease.
Converting Mixed Numbers to Standard Form, Five and nine tenths in standard form
A mixed number is a number that has a whole number part and a fractional part. To convert a mixed number to standard form, follow these steps:
- Multiply the whole number part by the denominator of the fraction.
- Add the numerator of the fraction to the product from step 1.
- Write the result as a decimal.
For example, to convert the mixed number 5 9/10 to standard form, we would do the following:
- 5 × 10 = 50
- 50 + 9 = 59
- 59/10 = 5.9
- The whole number part
- The decimal point
- The fractional part
- Write the decimal as a fraction.
- Multiply the numerator and denominator of the fraction by 10.
- Repeat step 2 until the denominator is a whole number.
- 0.123 = 123/1000
- 123/1000 × 10/10 = 1230/10000
- 1230/10000 × 10/10 = 12300/100000
- The digits to the left of the decimal point have a place value that is a multiple of 10.
- The digits to the right of the decimal point have a place value that is a fraction of 10.
Therefore, 5 9/10 in standard form is 5.9.
Understanding Standard Form
Standard form is the most common way of writing numbers. It is used in mathematics, science, and everyday life. Standard form is a convenient way to write numbers because it is easy to read and understand.
A number in standard form has three parts:
The whole number part is the number to the left of the decimal point. The decimal point is a period that separates the whole number part from the fractional part. The fractional part is the number to the right of the decimal point.
Decimal Expansion
Decimal expansion is a way of writing a number as a decimal that has an infinite number of digits. Decimal expansions are used to represent numbers that cannot be written as a fraction of two integers.
To convert a decimal to its expanded form, follow these steps:
For example, to convert the decimal 0.123 to its expanded form, we would do the following:
Therefore, the expanded form of 0.123 is 0.123000….
Place Value
Place value is the value of a digit in a number based on its position. The place value of a digit is determined by its position in the number, with the digit on the left having the highest place value and the digit on the right having the lowest place value.
In the decimal system, the place value of a digit is determined by its position to the left or right of the decimal point.
For example, in the number 5.9, the 5 has a place value of 5, and the 9 has a place value of 0.9.
Essential Questionnaire: Five And Nine Tenths In Standard Form
What is the standard form of five and nine tenths?
5.9
How do you convert a mixed number to standard form?
Multiply the whole number by the denominator of the fraction, add the numerator, and then divide the result by the denominator.
What is the place value of the 9 in 5.9?
0.9
