SME
Grade 8 Math · Expressions & Equations
Scientific notation
Use this for “Write 470,000 in scientific notation,” or a number in scientific notation in standard form.
Diagram
470,000 = 4.7 × 10⁵
10⁵ ≤ 470,000 < 10⁶
10⁵ = 100,000
10⁶ = 1,000,000
This is an example. Type your own values to start a new problem.
N
=
a
×
10
Formulas
N
=
a
×
10^
n
(number
=
number
from
1
up
to
10
×
10power
of
ten)
470,000
=
4.7 ×
10
5
n
=
exponent
of
the
power
of
ten
at
or
below
N
(power
of
ten
=
exponent
of
the
power
of
ten
at
or
below
number)
5 = exponent of the power of ten at or below 470,000
Assumptions
•
A number in scientific notation is a number from 1 up to 10 times a power of ten.
•
Each power of ten is ten times the one before it, so the ruler steps by × 10.
•
A negative power of ten is a number under 1: 10⁻⁴ = 0.0001.
•
A calculator may show 6.02E23 for 6.02 × 10²³.
Step-by-step
WE KNOW
N = 470,000 (number)
FIND
power of ten (n), number from 1 up to 10 (a)
Step 1 · Find power of ten (n)
Use n = exponent of the power of ten at or below N (power of ten = exponent of the power of ten at or below number)
Count how many places the point moves to leave one digit, not 0, before it.
n
=
exponent
of
the
power
of
ten
at
or
below
470,000
10
5
=
100,000
≤
470,000
<
1,000,000
=
10
6
n
=
5
Step 2 · Find number from 1 up to 10 (a)
Use N = a × 10ⁿ (number = number from 1 up to 10 × 10ᵖᵒʷᵉʳ of ten)
Divide by the power of ten to leave one digit, not 0, before the point.
470,000
=
a
×
10
5
a
=
470,000
10
5
a
=
470,000
100,000
a
=
4.7
Check
Put the numbers back in. Both sides should match.
470,000
=
4.7 ×
10
5
✓
5 = exponent of the power of ten at or below 470,000 ✓
Topic check
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Use this for “(3.1 × 10⁴) × (2 × 10⁶)”.
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Use this for “3.6 × 10⁵ + 2.9 × 10⁵” or “How much larger is 4.2 × 10⁸ than 7.5 × 10⁷?”
Powers of ten by name
Use this for “Match 1,000,000 to one million and to a power of ten.”