Numbers in scientific notation have two parts: a mantissa and an exponent which are multiplied together.
The mantissa has a value that is greater than or equal to 1 and less than 10 (ie it has a single non-zero digit before a decimal point).
The exponent is a power of 10 by which the mantissa is multiplied so that it has the same value as the original number.
When multiplying (or dividing) by a power of ten the digits of a number shift in the place value column table; however, on paper this is not easy to do (or visualise) so the (relative) effect on the decimal point is considered instead:
If a number is followed by a unit (metres, litres, grams, etc) then the number is converted and the unit follows the converted number.
To convert a number to scientific notation:
Also, if the number is not quite in scientific notation, that is, it has a number which does not have the decimal point after the first-non-zero digit but is multiplied by a power of 10, follow the above on the number before the x 10^... and then multiply the ten to the powers together by adding the powers
Examples:
123 → 1.23 × 10^2
123000 → 1.23 × 10^5
12.3 → 1.23 × 10^1
1.23 → 1.23 × 10^0
0.123 → 1.23 × 10^-1
0.000123 → 1.23 × 10^-4
12.3 × 10^5 = (1.23 × 10^1) × 10^5 = 1.23 × (10^1 × 10^5) = 1.23 × 10^(1 + 5) = 1.23 × 10^6
123 × 10^-3 = (1.23 × 10^2) × 10^-3 = 1.23 × (10^2 × 10^-3) = 1.23 × 10^(2 + -3) = 1.23 × 10^-1
To convert a number from scientific notation to normal notation move the decimal point the number of digits that is the power of the ten, inserting zeros if the digits run out. If the power is positive move the decimal point to the right; if negative to the left.
Examples
1.23 × 10^1 = 12.3
1.23 × 10^5 = 12300
1.23 × 10^0 = 1.23 (the decimal point moves 0 or no digits)
1.23 × 10^-1 = .123 = 0.123*
1.23 × 10^-5 = 0.0000123
* a zero is normally written before a leading decimal point to highlight the decimal point being there as leading zeros are not normally written.
Metric units include a multiplier in the letter preceding the unit, for example in km (kilometres) the k prefix means kilo- which is "× 1000" or "× 10^3".
To convert SI units to scientific notation, they are effectively in "not-quite" scientific notation and so the above is used by fist converting the unit multiplier to a power of 10. Examples:
1.23 km = 1.23 × 10^3 m
12.3 km = (1.23 × 10^1) × 10^3 m = 1.23 × (10^1 × 10^3) m = 1.23 × 10^4 m
123 mg = (1.23 × 10^2) × 10^-3 g = 1.23 × (10^2 × 10^-3) g = 1.23 × 10^-1 g
The most common Si prefix multipliers are:
pico- (p) = × 10^-12
nano- (n) = × 10^-9
micro- (µ) = × 10^-6
milli- (m) = × 10^-3
centi- (c) = × 10^-2
deci- (d) = × 10^-1
deka- (da) = × 10^1
hecto- (h) = × 10^2
kilo- (k) = × 10^3
mega- (M) = × 10^6
giga- (G) = × 10^9
Tera- (T) = × 10^12
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Do nothing! Standard form and scientific notation are the same.
Yes - you can always convert numbers to scientific notation - whether they're whole numbers, or decimals.
The steps, in order, will depend on what you wish to do: convert from normal to scientific notation, the converse, perform one of the basic operations of arithmetic on numbers in scientific notation.
It's best to convert those numbers from scientific notation to normal notation; that makes it easy to add them. After adding them, you can convert back to scientific notation if you want. Another option is to keep the numbers in scientific notation, but to convert them so that both have the same exponent.
Since .4428 is to the ten thousandths place, and scientific notation only takes an integer, a decimal point and then the numbers after it, the scientific notation would be 4.428 * 10-1