# How to convert decimal numbers into scientific notation

## How to convert decimals to scientific notation

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SAT Math Help » Arithmetic » Decimals » Other Decimals » How to convert decimals to scientific notation

Write  in scientific notation.

Explanation:

We want to move the decimal point to the place just after the first non-zero number, in this case 6, and then drop all of the non-significant zeros. We need to move the decimal point five spaces to the right, so our exponent should be negative.  If the decimal had moved left, we would have had a positive exponent.

In this case we get 6. 009 * 105.

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is equal to which of the following?

Explanation:

We need to convert  into a number of the form .

The trick is, however, figuring out what  should be. When you have to move your decimal point to the right, you need to make the decimal negative. (Note, though, when you multiply by a negative decimal, you move to the left. We are thinking in "reverse" because we are converting.)

Therefore, for our value, . So, our value is:

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is equal to which of the following?

Explanation:

The easiest way to do this is to convert each of your answer choices into scientific notion and compare it to . For each of the answer choices, this would give us:

When you convert, you add for each place that you move to the left and subtract for each place you move to the right. (Note that this is opposite of what you do when you multiply out the answer. We are thinking in "reverse" because we are converting.)

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Convert the decimal into scientific notation:

Explanation:

To convert a decimal into scientific notation, move the decimal point until you get to the left of the first non-zero integer. The number of places the decimal point moves is the power of the exponent, because each movement represents a "power of 10". The exponent will be positive if the original number is greater than zero, and negative if the original number is less than zero. For this example, move the decimal point four places to the right. Since the number is less than zero, the exponent is negative:

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Convert the decimal into scientific notation:

Explanation:

To convert a decimal into scientific notation, move the decimal point until you get to the left of the first non-zero integer. The number of places the decimal point moves is the power of the exponent, because each movement represents a "power of 10". The exponent will be positive if the original number is greater than zero, and negative if the original number is less than zero.

For this example, move the decimal point two places to the right. Since the number is less than zero, the exponent is negative:

Report an Error

Convert the decimal into scientific notation:

Explanation:

To convert a decimal into scientific notation, move the decimal point until you get to the left of the first non-zero integer. The number of places the decimal point moves is the power of the exponent, because each movement represents a "power of 10". The exponent will be positive if the original number is greater than zero, and negative if the original number is less than zero.

For this example, move the decimal point two places to the right. Since the number is less than zero, the exponent is negative:

Report an Error

Convert the decimal into scientific notation:

Explanation:

To convert a decimal into scientific notation, move the decimal point until you get to the left of the first non-zero integer. The number of places the decimal point moves is the power of the exponent, because each movement represents a "power of 10". The exponent will be positive if the original number is greater than zero, and negative if the original number is less than zero. For this example, move the decimal point four places to the right. Since the number is less than zero, the exponent is negative:

Report an Error

Convert the decimal into scientific notation:

Explanation:

To convert a decimal into scientific notation, move the decimal point until you get to the left of the first non-zero integer. The number of places the decimal point moves is the power of the exponent, because each movement represents a "power of 10". The exponent will be positive if the original number is greater than zero, and negative if the original number is less than zero.

For this example, move the decimal point seven places to the right. Since the number is less than zero, the exponent is negative:

Report an Error

Convert the decimal into scientific notation:

Explanation:

To convert a decimal into scientific notation, move the decimal point until you get to the left of the first non-zero integer. The number of places the decimal point moves is the power of the exponent, because each movement represents a "power of 10". The exponent will be positive if the original number is greater than zero, and negative if the original number is less than zero.

For this example, move the decimal point nine places to the right. Since the number is less than zero, the exponent is negative:

Report an Error

Convert the decimal into scientific notation:

Explanation:

To convert a decimal into scientific notation, move the decimal point until you get to the left of the first non-zero integer. The number of places the decimal point moves is the power of the exponent, because each movement represents a "power of 10". The exponent will be positive if the original number is greater than zero, and negative if the original number is less than zero. For this example, move the decimal point five places to the right. Since the number is less than zero, the exponent is negative:

Report an Error

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#### All SAT Math Resources

16 Diagnostic Tests 660 Practice Tests Question of the Day Flashcards Learn by Concept

## Scientific Notation Converter

Basic Calculator

Scientific Notation Converter

enter a number or scientific notation

Operand 1

= 3. 456 × 1011
scientific notation

= 3.456e11
scientific e notation

= 345.6 × 109
engineering notation
billion; prefix giga- (G)

= 3.456 × 1011
standard form

11
Order of Magnitude
for scientific and standard forms

= 345600000000
(real number)

= three hundred forty-five billion six hundred million
word form

Paste this link in email, text or social media.

Get a Widget for this Calculator

### Calculator Use

Convert a number to and from scientific notation, e notation, engineering notation, standard form, and real numbers. Enter a number or a decimal number or scientific notation and the calculator converts to scientific notation, e notation, engineering notation, standard form and word form formats. b where a is a number or decimal number such that the absolute value of a is greater than or equal to one and less than ten or, 1 ≤ |a| < 10. b is the power of 10 required so that the scientific notation is mathematically equivalent to the original number.

1. Move the decimal point in your number until there is only one non-zero digit to the left of the decimal point. The resulting decimal number is a.
2. Count how many places you moved the decimal point. This number is b.
3. If you moved the decimal to the left b is positive.
If you moved the decimal to the right b is negative.
If you did not need to move the decimal b = 0.
4. Write your scientific notation number as a x 10^b and read it as "a times 10 to the power of b. -4 = 3.456 x .0001 = 0.0003456

See the Scientific Notation Calculator to add, subtract, multiply and divide numbers in scientific notation or E notation.

To round significant figures use the Significant Figures Calculator.

To see how standard form is similar to scientific notation visit Standard Form Calculator.

If you need a scientific calculator see our resources on scientific calculators.

## Show numbers in exponential notation

Excel for Microsoft 365 Excel 2021 Excel 2019 Excel 2016 Excel 2013 Excel 2010 Excel 2007 More...Less

Exponential format displays the number in exponential form, replacing part of the number with E+ n , in which E (the exponent) multiplies the previous number by 10 to the nth point. For example, in scientific format, 12345678901 12345678901 displays 1.23E+10, i.e. from 1.23 to the 10th energy.

To apply scientific formatting to a number, follow the steps here.

1. Select the cells to be formatted. For more information, see Select cells, ranges, rows, and columns on a site.

Tip: To deselect cells, click any cell on the sheet.

2. On tab Home press the small button Additional next to the button Number.

3. In the list Category , select scientific . 4. Use the small arrows to indicate the decimal decimal places you want to display.

Tip: The number that is in the active cell of the selection on this site appears in the Sample field so that you can view the selected formatting options.

• To quickly format a number in scientific notation, select in the Number Format field (tab Home, group Number). Two decimal places are ordered by default for scientific notation.

• The format does not affect the actual value in the cell that Excel uses in calculations. The actual value can be seen in the formula bar.

• The maximum number precision limit is 15 digits, so the actual value shown in the formula bar may vary for large numbers (greater than 15 digits).

• To reset the number format, in the Number format field, select General (tab Home, group Number). Cells formatted using General, format do not have a specific number format. However, in the format General , exponential notation is used for large numbers (12 or more digits). To remove exponential notation from large numbers, you can apply a different number format, such as Number.

## Exponential notation calculator

 0 AC +/- ÷ 7 8 9 × 4 5 6 - 1 2 3 + 0 00 , =

### The exponential notation calculator will convert a number or expression into scientific notation and can also convert a number from exponential notation to ordinary and decimal fractions. To translate an expression into exponential notation, use the rules for entering numbers and expressions; to convert a number from exponential notation, enter numbers such as 2.3e+5, 5.8e-123, etc.

Representing the bit depth of the result No separationSpaceCommaApostrophePoint
Number of decimal places in scientific notation 123456781213141516171819202122232425

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#### What is exponential notation

Very large and very small numbers are more conveniently expressed in exponential notation. Exponential notation is the representation of real numbers in the form of mantissa and exponent. On a computer, such an entry can be represented as MEp, where

M is the mantissa

E is a letter meaning 10 n

p is an exponent (it can be either positive or )

Examples

14E+6 = 14 ∙ 10 6 = 14 ∙ 1000000 = 140000

16E-4 = 16

3. 96e+3 = 3.96 ∙ 10 3  = 3.96 ∙ 1000 = 3960

17.356e-4 = 17.356 ∙ 10 -4  = 17.356 ∙ 0.0001 = 0.0017356

0.23e+5 = 0.23 ∙ 10 5 = 0.23 ∙ 100000 = 23000

Pow (32, 7) = 32 7 = 3.43597384E+010

SQRT (√19344402 = 1.3 = 1.39081ED 3/5, 43.6) = 43.6√(3/5) = 9.88352183E-1

(1/2)-Sqrt(3.5)*206 = -3.848E+2

Sin(167, deg) = Sin( 167°) = 2.24951054E-1

multiplication and division of binary numbers 9009 potential φ of the electrostatic field
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