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Scientific Notation
Scientific notation is the expression of a number based on the largest exponent of 10 for its value, where the form is a decimal number A x 10n.
6,389 Questions
How do you calculate 45 to the power 0.3?
Approximated 3.133.
45^0.3 is the same as finding the 10th root of 45 to the 3rd power.
If you just need the approximate numerical value of an expression like this you can use google. Simply enter: 45^0.3 at the prompt and it will return 3.13302423373
More generally if you lack access to google, or to a calculator that can deal with fractional exponents, then you can make this calculation using logarithms.
log1045 = 1.65...
0.3*log1045 = 0.496...
10^0.496... = 3.1330...
And there are other, numerical methods. Ask again if you're interested.
How can you make scientific notation into numerals?
Scientific notation is a way of representing numbers, usually very large or very small, in the form
a*10b where 1 ≤|a| < 10 is a decimal number and b is an integer (negative or positive).
a is called the mantissa and b is called the exponent.
To convert a number in scientific notation to normal form:
- If b is positive, move the decimal point b places to the right in the number a - adding 0s at the end of the number, if required.
- If b is negative, move the decimal point b places to the left in the number a - adding 0s immediately after the decimal point, if required.
For example:
4.56*105 = 456000.
4.56*10-5 = 0.0000456
Is 2.35 10-3 scientific notation?
No, but 2.35*10-3 is. The difference may be due purely to the inadequacy of the browser used to post questions.
(a)
1. Let x = the repeating decimal. (a) x = 0.151 515 151 5…
2. Multiply
x by the power of 10 that
contains the same number of zeros as
there are digits in the repeating pattern.
The pattern contains 2 digits so
multiply by 100.
100
x = 15.151 515 15…
3. Subtract
x from the new value. 100x - x = 15.151 515 15 - 0.151 515 15
99
x = 15
4. Solve the linear equation found, putting
your answer in simplest (improper if
necessary) fraction form.
x
=
=
5. Check your answer by doing the division
on your calculator.
5
÷ 33 = 0.15151515…
(b)
1. Let x = the repeating decimal. (b) x = 1.244 444 44…
2. Multiply
x by the power of 10 that
contains the same number of zeros as
there are digits in the repeating pattern.
The pattern contains 1 digit so
multiply by 10.
10
x = 12.444 444…
3. Subtract
x from the new value. 10x - x = 12.444 444 - 1.244 444
9
x = 11.2
4. Solve the linear equation found, putting
your answer in simplest (improper if
necessary) fraction form.
x
= = =
5. Check your answer on your calculator. 56
÷ 45 = 1.244 44…
(c)
1. Let x = the repeating decimal. (c) x = 0.114 211 421 142…
2. Multiply
x by the power of 10 that
contains the same number of zeros as
there are digits in the repeating pattern.
The pattern contains 4 digits so
multiply by 10 000.
10 000
x = 1142.114 211 421 142…
3. Subtract
x from the new value. 10 000x - x = 1142.114 211 421 142
- 0.114 211 421 142
9999
x = 1142
4. Solve the linear equation found, putting
your answer in simplest (improper if
necessary) fraction form.
x
=
5. Check your answer on your calculator. 1142
÷ 9999 = 0.114 211 421 142…
How do you write two and fourteen thousandths in standard form?
Two and fourteen thousandths (2.014) in standard form is 2.014 × 100
What is 2.6105 written in standard notation?
It is 2.6105 but if you must, you can write it as 2.6105*10^0.
What is nine hundred twenty-five thousandths standard form?
Nine hundred twenty-five thousandths (0.925) standard form is 9.25 × 10-1
How do you write one hundred six thousand five hundred and five in standard form?
One hundred six thousand five hundred and five (106,505*) in standard form is 1.06505 × 105
* this is the standard notation
