Edexcel IGCSE Math A 1.3.HA Converting Recurring Decimals to Fractions

E.g.
$$x=4.57 \ldots . \text { and } 100 x=457.57 \ldots .$$

or
$$10 x=45.757 . . . . \text { and } 1000 x=4575.7 . . .$$

or
$$\begin{aligned} & x=0.57 \ldots . \text { and } 100 x=57.57 \ldots & \text { or } & 10 x=5.757 \ldots . \text { and } 1000 x=575.7 \ldots . \end{aligned}$$

M1
$$\begin{aligned} \text { for selecting } 2 \text { recurring decimals that } \text { when subtracted give a whole number or } \text { terminating decimal eg } 453 \text { or } 4530 \text { etc } \text { eg } 100 x=457.57 \ldots \text { and } x=4.57 \ldots \text { or } 1000 x=4575.7 \ldots \text { and } 10 x=45.757 \ldots \text { with intention to subtract. (If recurring } \text { dots not shown then allow } 10 x=45.757 \text {, } 100 x=457.57 \text {, and } 1000 x=4575.7 \text { to at } \text { least } 5 \text { sf) } \text { or } 4+0.5757 \text { and eg } x=0.57 \ldots, 100 x= 57.57 \ldots \text { with intention to subtract. } \end{aligned}$$

E.g.
$$\begin{aligned} & 100 x-x=457.57 \ldots-4.57 \ldots=453 \text { and } & \frac{453}{99}=\frac{151}{33} \text { or } 4 \frac{19}{33} & \text { or } \end{aligned}$$$$\begin{aligned} & 1000 x-10 x=4575.7 \ldots-45.757 \ldots=4530 \text { and } & \frac{4530}{990}=\frac{151}{33} \text { or } 4 \frac{19}{33} \end{aligned}$$

or
$$\begin{aligned} & 100 x-x=57.57 \ldots-0.57 \ldots=57 \text { and } \frac{57}{99} \text { or } \frac{19}{33} & \text { (so) } 4 . \ddot{5} \dot{7}=4 \frac{19}{33} \end{aligned}$$

or
$$\begin{aligned} & 1000 x-10 x=575.7 \ldots-5.757 \ldots=570 \text { and } & \frac{570}{990} \text { or } \frac{57}{99} \text { or } \frac{19}{33} \text { (so) } 4 . \dot{5} \overrightarrow{7}=4 \frac{19}{33} \end{aligned}$$

Shown

A1

for completion to $\frac{151}{33}$ or $4 \frac{19}{33}$