Write 2 67 5 In Standard Form

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Write #6.7xx10^(-5)# in standard form?

1 Answer

Explanation:

In scientific notation, we write a number so that it has single digit to the left of decimal sign and is multiplied by an integer power of #10#.

In other words, in scientific notation, a number is written as #axx10^n#, where #1<=a<10# and #n# is an integer and #1<=a<10#.

To write the number in normal or standard notation one just needs to multiply by the power #10^n# (or divide if #n# is negative). This means moving decimal #n# digits to right if multiplying by #10^n# and moving decimal #n# digits to left if dividing by #10^n# (i.e. multiplying by #10^(-n)#).

In the given case, as we have the number as #6.7xx10^(-5)#, we need to move decimal digit to the left by five points. For this, let us write #6.7# as #0000006.7# and moving decimal point five points to left means #0.000067#

Hence in standard form #6.7xx10^(-5)=0.000067#

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Scientific Notation Calculator

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Scientific notation

Scientific notation is a way to express numbers in a form that makes numbers that are too small or too large more convenient to write. It is commonly used in mathematics, engineering, and science, as it can help simplify arithmetic operations. In scientific notation, numbers are written as a base, b, referred to as the significand, multiplied by 10 raised to an integer exponent, n, which is referred to as the order of magnitude:

b × 10ⁿ

Below are some examples of numbers written in decimal notation compared to scientific notation:

Engineering notation

Engineering notation is similar to scientific notation except that the exponent, n, is restricted to multiples of 3 such as: 0, 3, 6, 9, 12, -3, -6, etc. This is so that the numbers align with SI prefixes and can be read as such. For example, 10³ would have the kilo prefix, 10⁶ would have the mega prefix, and 10⁹ would have the giga prefix. Note that the decimal place of the number can be moved to convert scientific notation into engineering notation. For example:

1.234 × 10⁸ (scientific notation)

can be converted to:

123.4 × 10⁶ (engineering notation)

E-notation

E-notation is almost the same as scientific notation except that the '× 10' in scientific notation is replaced with just 'E.' It is used in cases where the exponent cannot be conveniently displayed. It is written as:

bEn

Write 2 67 5 In Standard Form Converter

where b is the base, E indicates 'x 10' and the n is written after the E. Below is a comparison of scientific notation and E-notation:

Write 2 67 5 In Standard Form Example

Write 2 67 5 In Standard Form Calculator

The 'E' can also be written as 'e' which is what is used by this calculator. It can also be written in other ways depending on the context, such as being represented differently in different programming languages.