How do you convert scientific notation into standard form?

Answer 1

Expand the 10exponent to the full number (eg 103 = 10 x 10 x 10 = 1000) and then multiply the two numbers together - the mantissa x 10exponent. If the exponent is negative, take the reciprocal of the power, eg 10-3 = 1 ÷ (10 x 10 x 10) = 1 ÷ 1000; multiplying by (1 ÷ 1000) is the same as dividing by 1000.

This can be done most easily by moving the decimal point the exponent number of digits to the right if positive and left if negative, inserting zeros when running out of digits.

Examples:

1.234 x 102 = 1.234 x (10 x 10) = 1.234 x 100 = 123.4

Alternatively: 1.234 x 102 exponent is 2, so move dp 2 digits right: 1.234 → 123.4

1.234 x 10-2 = 1.234 x (1 ÷ (10 x 10)) = 1.234 x (1 ÷ 100) = 1.234 ÷ 100 = 0.01234

Alternatively: 1.234 x 10-2 exponent is -2, so move dp 2 digits left, inserting one zero: 1.234 → 0.01234