Standard Form (GCSE Maths)

Combine to get $10 \times 10^6$ and adjust into proper standard form (the coefficient must be between $1$ and $10$):

Since the powers of 10 are identical ($10^4$), factor it out and add the coefficients:

Place the decimal point after the first non-zero digit: $3.6$.

Count the places moved to the right (3 places) to find the negative power of $10$.

Place the decimal point after the first digit: $7.2$.

Count the places moved to the left ($6$ places) for the power of $10$.

Place the decimal point after the first non-zero digit to create a number between $1$ and $10$:

Count the number of places the decimal point moved to the left ($3$ places) to find the positive power of $10$.

• Combine the results to get $12 \times 10^7$.
• To write in standard form, the coefficient must be between 1 and 10:

The powers are the same, so add the coefficients:

Keep the common power of $10$.

The powers are the same, so subtract the coefficients:

Keep the common power of $10$.

Combine the components to get $24 \times 10^4$, then adjust into standard form:

• The powers are different ($10^5$ and $10^3$). To add the numbers, they must be expressed with the same power.
• Converting $3 \times 10^3$ to match the larger power ($10^5$) gives:

Now that both terms have $10^5$, add the coefficients:

Combine the parts to get $15 \times 10^7$. To write this in standard form, move the decimal point one place to the left:

To add the numbers, we first rewrite them so they share the same power of 10:

Now that both terms have the same power of 10, we can add the coefficients:

• We have $502 \times 10^2$.
• To write this in standard form, we adjust the coefficient to be between $1$ and $10$:

Convert $6 \times 10^6$ into $60 \times 10^5$ so that the powers match:

Combine the result to get $56 \times 10^5$ and adjust to standard form: